Question

Find the smallest number which when divided 63 90 and 135 leaves 11 as remainder.

Answer 1

Step-by-step explanation:

Given:Find the smallest number which when divided 63, 90 and 135 leaves 11 as remainder.

To find:smallest number which when divided 63, 90 and 135 leaves 11 as remainder.

Solution:

To find the smallest number which when divided 63, 90 and 135 leaves 11 as remainder,

first find the LCM of 63,90 and 135

$63 = 3 \times 3 \times 7 \\ 90 = 2 \times 3 \times 3 \times 5 \\ 135 = 3 \times 3 \times 3 \times 5 \\ \\ LCM(63, \: 90, \: 135) = 2 \times {3}^{3} \times 5 \times 7 \\ \\LCM(63, \: 90, \: 135) = 2 \times 27 \times 35 \\\\ LCM(63, \: 90, \: 135) = 1890$

Now,add the common remainder

$1890 + 11 \\ \\ = \bold{1901}$

Thus,

1901 is the smallest number which when divided 63 90 and 135 leaves 11 as remainder.

Hope it helps you.

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