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The least number, when lessened (decreased) by 5, to be divisible by 36, 48, 21, and 28 is
Correct Answer: 1013
The number reduced by 5 must be a common multiple of 36, 48, 21 and 28, so the smallest such value is their LCM. Since $$36 = 2^2 \times 3^2$$, $$48 = 2^4 \times 3$$, $$21 = 3 \times 7$$ and $$28 = 2^2 \times 7$$, the LCM is $$2^4 \times 3^2 \times 7 = 1008$$. Adding back the 5 gives $$1008 + 5 = 1013$$.
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