H.C.F Of 3240, 3600 And A Third Number Is 36 And Their L.C.M Is 24 * 35 * 52 * 72. The Third Number Is__________

Hamad Problems on L.C.M and H.C.F 20/02/2021

A. 2² * 3⁵ * 7²
B. 2² * 5³ * 7²
C. 2⁵ * 5² * 7²
D. 2³ * 3⁵ * 7²

Explanation:

3240 = 2³ * 3⁴ * 5; 3600 = 2⁴ * 3² * 5²

H.C.F = 36 = 2² * 3²

Since H.C.F is the product of lowest powers of common factors, so the third number must have (2² * 3² ) as its factor.

Since L.C.M is the product of highest powers of common prime factors, so the third number must have 3⁵ and 7² as its factors.

Third number = 2² * 3⁵ * 7²

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