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The check is done easily without finding then numbers. Since, LCM is a multiple of HCF, ie., 378 = 21 * 18, the answer is yes.

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Let the numbers be A and B. product of two numbers = product of LCM and HCF. A * B = 18 * 378

let A = 18 * M and B = 18 * N A*B = 18 * 18 * M * N = 18 * 378 = 18 * 18 * 3 * 7 * 1

There are two combinations of numbers for which this is true: 18, 378. and 54 , 126

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

You should know that HCF of two numbers is always a factor of the LCM.

(Why this happens is: HCF is a factor of both the numbers. Both the numbers are factors of LCM. Thus HCF is also a factor of LCM and it is always true.)

Your answer: Check whether 18 is a factor of 378. 378 ÷ 18 = 21, remainder = 0

Since remainder is 0, 18 is a factor of 378. So It is possible for the HCF and LCM of two number to be 18 and 378 respectively