Question

what is the smallest number which when divided by 24, 36 and 54 givens a remainder of 5 each times?​

Answer 1

Answer:

221

Step-by-step explanation:

GIVEN=

THREE NUMBERS=24,36,54

TO FIND=

SMALLEST NUMEBER WHICH GIVES REMAINDER 5

SOLUTION=

Let's factorize,  

24 = 2x2x2x3

36 = 2x2x3x3

54 = 2x3x3x3

The smallest number divisible by all 24, 36, 54 is:

LCM(24, 36, 54) = 216

Thus, to get 5 as remainder, we need to add 5 to 216.

(as 216 is the smallest number which gives remainder 0 when divided by 24 or 36 or 54)

216 + 5 = 221

For 12, 221 gives 18 as quotient and 5 as remainder

For 36, 221 gives 6 as quotient and 5 as remainder

For 54, 221 gives 4 as quotient and 5 as remainder

Hence, 221 is required number.

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