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11-07-2020
Mathematics

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The HCF of 56, x and 154 is 14 and their LCM is 4312. Find the smallest possible integer x

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PollyP52 PollyP52

11-07-2020

Answer:

Smallest possible x = 98.

Step-by-step explanation:

4312 = 2 * 2 * 2 * 7 * 7 * 11

56 = 2 *2 * 2 * 7

154 = 2 * 7 * 11

Because the HCF is 14:-

x = = 2 * 7 OR 2 * 7 * other prime number(s).

As there are 2 7's in the prime factors of 4312 there must also be another 7 in the prime factors of x.

x = 2 * 7 * 7 = 98.

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