Question

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

Answer 1

Step-by-step explanation:

Let x be odd such that LCM{x,40}=1400 . Since 1400=23×52×7 , then x∈{5m×7n∣(m,n)∈{0,1,2}×{0,1}} . By testing these values, we find that x=175 .

sol.40 = 2^3 * 5

1400 = 2^3 * 5^2 * 7

LCM(2^3 * 5, 5^2 * 7) = 1400

so x = 175

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