3 H.C.F. of 3240, 3600 and a third number is 36 and their L.C.M. is 24 x 35 x 52 x 72. The third number is (M.A.T., 2005)
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Answer:
Let us see how to solve it.
Explanation:
To solve this question, we first need to express the numbers in the form of prime factors.
3240 = 23 × 34 × 5
3600 = 24 × 32 × 52
The HCF is 36 which can be expressed as 22 × 32 by prime factorization.
The LCM in the form of prime factors is 24 × 35 × 52 × 72
By the definition, we know that HCF is the product of the lowest power of common prime factors. This means that the third number must include the HCF, which is 22 × 32.
Also, LCM is the product of the highest power of common prime factors implying that the third number must include 22 × 72
Thus, the third number is 22 × 35 × 72.
Therefore, the third number is 47628 (22 × 35 × 72)
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