Aptitude - H.C.F and L.C.M
16.
The product of two co-primes is 117. Their L.C.M. should be
Answer
H.C.F of co-primes = 1.
H.C.F x L.C.M = Their product = 117
∴ 1 x L.C.M. = 117 ⇒ L.C.M. = 117
Answer :
Option BExplanation :
H.C.F of co-primes = 1.
H.C.F x L.C.M = Their product = 117
∴ 1 x L.C.M. = 117 ⇒ L.C.M. = 117
17.
H.C.F. of 3240, 3600 and a third number is 36 and their L.C.M is (24 x 35 x 52 x 72 ) . The third number is :
Answer
3200 = 23 x 34 x 5
3600 = 24 x 32 x 52
H.C.F. = 36 = 22 x 32
L.C.M. = 24 x 35 x 52 x 72
∴ 3rd number must have 22 x 32 as its factor.
∴ 3rd number = 22 x 35 x 72
Answer :
Option CExplanation :
3200 = 23 x 34 x 5
3600 = 24 x 32 x 52
H.C.F. = 36 = 22 x 32
L.C.M. = 24 x 35 x 52 x 72
∴ 3rd number must have 22 x 32 as its factor.
∴ 3rd number = 22 x 35 x 72
18.
The L.C.M. of two numbers is 2310 and their H.C.F. is 30. If one of the numbers is 210, then the other is :
Answer
Let the second number be p. Then,
2310 x 30 = 210 x p ⇒ p = 2310 x 30 210 = 330
Hence, the second number is 330.
Answer :
Option AExplanation :
Let the second number be p. Then,
2310 x 30 = 210 x p ⇒ p = 2310 x 30 210 = 330
Hence, the second number is 330.
19.
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 seconds respectively. In 30 minutes, how many times do they toll together ?
Answer
L.C.M. of 2, 4, 6, 8, 10, 12 = 120 i.e. 2 minutes
After every 2 minutes they toll together.
∴ Number of times they toll in 30 minutes =
30 2 + 1 
times = 16 times.
Answer :
Option DExplanation :
L.C.M. of 2, 4, 6, 8, 10, 12 = 120 i.e. 2 minutes
After every 2 minutes they toll together.
∴ Number of times they toll in 30 minutes =
30 2 + 1 times = 16 times. 20.
The least perfect square number divisible by 3, 4, 5, 6 and 8 is :
Answer
L.C.M. = (3 x 2 x 2 x 5 x 2) = (3 x 2 x 22 x 5)
Required number = (32 x 22 x 22 x 52) = 3600
Answer :
Option DExplanation :
L.C.M. = (3 x 2 x 2 x 5 x 2) = (3 x 2 x 22 x 5)
Required number = (32 x 22 x 22 x 52) = 3600
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