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Mathematics

Find the least number which when increased by 15 is exactly divisible by 15, 35 and 48.

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Answer

First, we find the LCM of 15, 35 and 48.

215, 35, 48
215, 35, 24
215, 35, 12
215, 35, 6
315, 35, 3
55, 35, 1
71, 7, 1
1, 1, 1

LCM of 15, 35 and 48 = 2 × 2 × 2 × 2 × 3 × 5 × 7 = 1680.

Thus, 1680 is the least number exactly divisible by 15, 35 and 48.

According to given condition, the required number when increased by 15 gives 1680.

The required number = 1680 − 15 = 1665.

Hence, the required least number is 1665.

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