Question

Find the least number that, when divided by 44 and 66, leaves the remainder 6 in each case.

Answer 1

Answer:

The smallest number which when divided by 35, 56 and 91 = LCM(35,56,91)

35=5×7

56=2

3

×7

91=7×13

LCM=2

3

×5×7×13=3640

The smallest number that when divided by 35, 56, 91 leaves a remainder 7 in each case = 3640 + 7 = 3647.

Answer 2

To find the least number that when divided by 44 and 66 leaves a remainder 6 ,we must first find the L.C.M. of 44 and 66 and then add 6 to it.

We need the least multiples of 44 and 66.

44= 2x2x11
66= 2x3x11

L.C.M of 44 and 66= 11x2x2x3
L.C.M (44 and 66) = 132

The required number = 132+6
= 138

Hence 138 is the smallest number, with a remainder of 6 in each case when divided by 44 and 66.