Let x be the greatest number which, when dividing 31, 61 and 91, leaves the same remainder. The LCM of x and 48 is:
Given:
x leaves same remainder when dividing 31, 61, 91
Formula Used:
If a number leaves same remainder, it divides the differences.
LCM(a, b) = (a × b) ÷ HCF(a, b)
Solution:
Differences:
61 − 31 = 30
91 − 61 = 30
91 − 31 = 60
Greatest divisor of 30 and 60
→ x = HCF(30, 60) = 30
LCM(x, 48) = LCM(30, 48)
HCF(30, 48) = 6
LCM = (30 × 48) ÷ 6 = 240
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