Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the LCM of 10, 12, 15?
💡
Step-by-Step Explanation & Concept Rationale
The smallest number divisible by 10, 12, and 15 is 60.
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
The least square number which is divisible by 2, 3, 4, 5 and 6 is
💡
Step-by-Step Explanation & Concept Rationale
LCM(2,3,4,5,6)=60. The smallest perfect square multiple of 60 is 900.
Q. 3
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
The least number of four digits which is exactly divisible by 2, 3, 4, 5, 6 and 7 is
💡
Step-by-Step Explanation & Concept Rationale
LCM(2,3,4,5,6,7)=420. The smallest 4-digit multiple of 420 is 1260.
Q. 4
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
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.
💡
Step-by-Step Explanation & Concept Rationale
LCM(16,20,25,45)=3600. 3600×2+3=7203 is divisible by 21.
Q. 5
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Remainder 25 when div by 35, 35 when div by 45, 45 when div by 55.
💡
Step-by-Step Explanation & Concept Rationale
Common difference is 10. LCM(35,45,55)−10=3465−10=3455.
Q. 6
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
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.
💡
Step-by-Step Explanation & Concept Rationale
LCM(8,12,16)=48. 48×3+3=147, which is divisible by 7.
Q. 7
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
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.
💡
Step-by-Step Explanation & Concept 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
\(35 - 25 = \mathbf{10}\)
\(45 - 35 = \mathbf{10}\)
\(55 - 45 = \mathbf{10}\)
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
Q. 8
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the LCM of 15, 45, 60?
💡
Step-by-Step Explanation & Concept Rationale
Multiples of 60: 60, 120, 180. 180 is the first divisible by both 15 and 45.
Q. 9
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
The LCM of 15, 24, 30, 40 is:
💡
Step-by-Step Explanation & Concept Rationale
120 is the smallest integer divisible by all four numbers.
Q. 10
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
LCM of 12, 36, 6 and 9 is:
💡
Step-by-Step Explanation & Concept Rationale
36 is the smallest number that is a multiple of 12, 36, 6, and 9.
Q. 11
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest number of four digit which will leave a remainder of 1 when divided by any number 5, 9, 12, 15 or 18?
💡
Step-by-Step Explanation & Concept Rationale
LCM(5,9,12,15,18)=180.
Largest 4-digit multiple of 180 is 9900.
9900+1=9901.
Largest 4-digit multiple of 180 is 9900.
9900+1=9901.
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