Question

Find an odd natural numbers x such that LCM (x, 40) = 1400​

Answer 1

175

Explanation:

so, the LCM is the combination of the longest chains of the prime factors in every number.

40 : 2, 2, 2, 5

1400 / 40 = 35

35 : 5, 7

but LCM(35, 40) = 2×2×2×5×7 = 280

and not 1400.

what is missing ?

1400 / 280 = 5

aha, another prime factor 5 is missing to get 1400.

x : 5, 5, 7

so, x = 5×5×7 = 175

LCM(175, 40) = 2×2×2×5×5×7 = 1400