Let x be the greatest number which, when divided by 31, 61 and 91, leaves the same remainder. The LCM of x and 48 is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 240 .
31, 61 and 91 leave the same remainder when divided by x
So, x divides the differences between them
61 − 31 = 30
91 − 61 = 30
91 − 31 = 60
Hence x = HCF of 30 and 60 = 30
LCM of 30 and 48
30 = 2 × 3 × 5
48 = 24 × 3
LCM = 24 × 3 × 5 = 16 × 15 = 240