Find the least number which when divided by 12, 16, 24 and 36 leaves remainder 7

Example 14 - Chapter 3 Class 6 Playing with Numbers

Last updated at Jan. 3, 2019 by

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Example 14 Find the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case. Least number when divided by 12, 16, 24, 36 & leaves remainder 0 = LCM of 12, 16, 24, 36 So, LCM leaves remainder 0 Now, in the question We are asked smallest number which leaves remainder 7 So, Required number will be 7 more than LCM ∴ Required number = LCM + 7 Finding LCM of 12, 16, 24, 36 ∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 = 16 × 9 = 144 So, Required Number = LCM + 7 = 144 + 7 = 151

`151``121``141``111`

Answer : A

Solution : To solve this question, we first have to find `LCM` of `12,16,24 and 36`.
`LCM` of these 4 numbers will be `144`. Please refer to video to find `LCM`.
So, least number that leaves remainder `7` when divided by `12, 16, 24 and 36` `= 144+7 = 151`

Find the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case.

Solution

We first find the LCM of 12, 16, 24, and 36 as follows:

Thus, LCM = 2 × 2 × 2 × 2 × 3 × 3 = 144

144 is the least number which when divided by the given numbers will leave remainder 0 in each case. But we need the least number that leaves remainder 7in each case.
Therefore, the required number is 7 more than 144.

The required least number = 144 + 7 = 151.

Concept: Lowest Common Multiple

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