Question

Which is the smallest number that is a perfect square which can be divided by 14, 24, 35
and 77?

Answer 1

The smallest number divisible by 14,24,35 and 77 is their L.C.M ., which is equal to 9240.

Factorising 9240 into pairs of equal Factors:

9240 = 2³ × 3¹ × 5¹ × 7¹ × 11¹

/* Grouping them into pairs of equal Factors.

9240 = (2×2)×2×3×5×7×11

The factors 2,3,5,7,11 are not paired .

To make 9240 into a perfect square , we have to multiply it by 2×3×5×7×11., i.e., by 2310.

The perfect square is 9240 × 2310, which is equal to 21344400 = (4620)².

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