Aptitude - H.C.F and L.C.M
6.
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is :
Answer
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 − 399) = 9600.
Answer :
Option CExplanation :
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 − 399) = 9600.
7.
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is :
Answer
Let the numbers be 3x , 4x and 5x .
Then, their L.C.M. = 60x .
So, 60x = 2400 or x = 40.
∴ The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
Answer :
Option AExplanation :
Let the numbers be 3x , 4x and 5x .
Then, their L.C.M. = 60x .
So, 60x = 2400 or x = 40.
∴ The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
8.
252 can be expressed as a product of primes as :
Answer
Clearly, 252 = 2 x 2 x 3 x 3 x 7.
Answer :
Option AExplanation :
Clearly, 252 = 2 x 2 x 3 x 3 x 7.
9.
The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is :
Answer
Required number = (L.C.M. of 12, 15, 20, 54) + 8
= 540 + 8 = 548.
Answer :
Option DExplanation :
Required number = (L.C.M. of 12, 15, 20, 54) + 8
= 540 + 8 = 548.
10.
The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is :
Answer
Required number = H.C.F. of (1657 − 6) and (2037 − 5)
= H.C.F. of 1651 and 2032 = 127.
Answer :
Option BExplanation :
Required number = H.C.F. of (1657 − 6) and (2037 − 5)
= H.C.F. of 1651 and 2032 = 127.
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