Find the least number, which gives the same remainder 5, when divided by 6, 10, 15 and 24.
Given:
We need to find the least number that leaves a remainder of 5 when divided by 6, 10, 15, and 24.
Solution:
Find the LCM of 6, 10, 15, and 24:
Prime factorization:
6 = 2 × 3
10 = 2 × 5
15 = 3 × 5
24 = 2³ × 3
LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120
The required number is LCM + remainder = 120 + 5 = 125
Therefore, the least number that leaves a remainder of 5 when divided by 6, 10, 15, and 24 is 125.
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