LCM

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๐Ÿ“˜ Comprehensive Syllabus & Examination Guide

LCM

Official curriculum roadmap, subject/topic distribution, negative marking rules, pacing guidelines, and solved sample questions.

๐ŸŽฏ Mapped Subjects & Topic Question Distribution

Total Question Pool 100%
11 MCQs
Combined Active Syllabus
LCM
11 MCQs
Topic Pool
๐Ÿ“Š Question Pool Structure
11 MCQs across fundamental, intermediate, and advanced concept tiers.
โšก Recommended Pacing
45 to 60 seconds per MCQ. Flag complex problems and preserve 10 minutes for final revision.
โš–๏ธ Scoring & Negative Marking
+1 mark per correct answer. In competitive tests with negative marking, -0.25 applies for incorrect guesses.

๐Ÿ’ก Strategic Preparation & Exam Hall Guidelines

To maximize your score on LCM, candidates are advised to follow a structured three-pass approach. In the First Pass, solve all direct recall and formula-based questions within 30 seconds each to secure foundational marks. In the Second Pass, tackle multi-step analytical and quantitative reasoning problems. In the Third Pass, review marked questions and verify calculations.

Practice with the interactive player below to evaluate your speed and accuracy under real exam pressure. Every question features full mathematical formulas, step-by-step worked solutions, and conceptual explanations vetted by Apex Rankers Academy subject matter specialists.

Ready to test your knowledge? Launch interactive 1-by-1 practice with instant feedback, bookmarking, and step-by-step rationales.
Solved Blueprint Examples

๐Ÿ“ Pre-Rendered Solved Sample Questions & Detailed Solutions

Showing 10 solved representative questions

Review the solved problems below to understand question phrasing, answer choices, and step-by-step solution logic prior to starting the full interactive practice drill:

Sample Question 1
LCM Medium • Quantitative Aptitude Test
What is the LCM of 10, 12, 15?
A 120
B 60
C 15
D 150
โœ“ Correct Answer: B - 60
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
The smallest number divisible by 10, 12, and 15 is 60.
Sample Question 2
LCM Medium • Quantitative Aptitude Test
The least square number which is divisible by 2, 3, 4, 5 and 6 is
A 800
B 900
C 1000
D 1200
โœ“ Correct Answer: B - 900
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
LCM(2,3,4,5,6)=60. The smallest perfect square multiple of 60 is 900.
Sample Question 3
LCM Medium • Quantitative Aptitude Test
The least number of four digits which is exactly divisible by 2, 3, 4, 5, 6 and 7 is
A 1200
B 1250
C 1260
D 1300
โœ“ Correct Answer: C - 1260
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
LCM(2,3,4,5,6,7)=420. The smallest 4-digit multiple of 420 is 1260.
Sample Question 4
LCM Medium • Quantitative Aptitude Test
A heap of stones can be made up into groups of 21 but when made up into groups of 16, 20, 25 and 45 there are three stones left in each case. How many stones at least there can be in the heap.
A 7203
B 7200
C 7500
D 7000
โœ“ Correct Answer: A - 7203
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
LCM(16,20,25,45)=3600. 3600ร—2+3=7203 is divisible by 21.
Sample Question 5
LCM Medium • Quantitative Aptitude Test
Remainder 25 when div by 35, 35 when div by 45, 45 when div by 55.
A 2000
B 2515
C 3005
D 3455
โœ“ Correct Answer: D - 3455
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
Common difference is 10. LCM(35,45,55)โˆ’10=3465โˆ’10=3455.
Sample Question 6
LCM Medium • Quantitative Aptitude Test
Find the least number which when divided by 8, 12 and 16 leaves 3 as remainder in each case but when divided by 7 leaves no remainder.
A 140
B 147
C 150
D 160
โœ“ Correct Answer: B - 147
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
LCM(8,12,16)=48. 48ร—3+3=147, which is divisible by 7.
Sample Question 7
LCM Medium • Quantitative Aptitude Test
Find the least number which, when divided by 35 leaves remainder 25, when divided by 45 leaves remainder 35, and when divided by 55 leaves remainders 45.
A 2000
B 2515
C 3005
D 3455
โœ“ Correct Answer: D - 3455
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
Notice that in each case, the difference between the divisor and its respective remainder is a constant 10:
\(35 - 25 = \mathbf{10}\)
\(45 - 35 = \mathbf{10}\)
\(55 - 45 = \mathbf{10}\)

When a problem features a constant difference (\(d\)) between all divisors and remainders, the least required number is found using the formula:
\(\text{Required Number}=\text{LCM}(\text{Divisors})-d\)

Step-by-Step CalculationFind the Least Common Multiple (LCM) of 35, 45, and 55:
Prime factorization of \(35 = 5 \times 7\)
Prime factorization of \(45 = 3 \times 3 \times 5 = 3^2 \times 5\)
Prime factorization of \(55 = 5 \times 11\)\(\text{LCM} = 3^2 \times 5 \times 7 \times 11 = 9 \times 5 \times 7 \times 11 = \mathbf{3465}\)
Subtract the constant difference (10):
\(3465 - 10 = \mathbf{3455}\)
Verification
\(3455 \div 35 = 98\) with a remainder of 25
\(3455 \div 45 = 76\) with a remainder of 35
\(3455 \div 55 = 62\) with a remainder of 45
Sample Question 8
LCM Medium • Quantitative Aptitude Test
What is the LCM of 15, 45, 60?
A 60
B 90
C 810
D 180
โœ“ Correct Answer: D - 180
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
Multiples of 60: 60, 120, 180. 180 is the first divisible by both 15 and 45.
Sample Question 9
LCM Medium • Quantitative Aptitude Test
The LCM of 15, 24, 30, 40 is:
A 360
B 240
C 120
D 480
โœ“ Correct Answer: C - 120
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
120 is the smallest integer divisible by all four numbers.
Sample Question 10
LCM Medium • Quantitative Aptitude Test
LCM of 12, 36, 6 and 9 is:
A 108
B 144
C 72
D 36
โœ“ Correct Answer: D - 36
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
36 is the smallest number that is a multiple of 12, 36, 6, and 9.
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