Question

Find the smallest number which when divided by 24, 36 and 64 leaves 4 as remainder in each case. ​

Answer 1

580

Step-by-step explanation:

24 = 2×2×2×3

36 = 2×2×3×3

64 = 2×2×2×2×2×2

The smallest number divisible by all 24, 36, 64 is:

LCM(24, 36, 64) = 576

Thus, to get 4 as remainder, we need to add 4 to 576.

(as 576 is the smallest number which gives remainder 0 when divided by 24 or 36 or 64)

576 + 4 = 580

For 24, 580 gives 24 as quotient and 4 as remainder

For 36, 580 gives 16 as quotient and 4 as remainder

For 64, 580 gives 9 as quotient and 4 as remainder

Hence, 580 is required number.

Answer 2

Answer:

In a) LCM of 24, 36, 64 is 576 hence 580 is that number which is divisible by three three and give 4 as a reminder. In b) LCM of three these given numbers is 600 so, the number is 620. In c) LCM is 1200 so, the number is 1190.