Find the LCM and HCF of each of the pairs of integer given in by applyinf the prime factorisation method 56 and 77
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Answers
Answer:
I too was struggling with this problem and arrived at a general solution for finding a pair of numbers given the HCF and the LCM. It is essentially the reverse of finding the LCM of two numbers by the use of a prime factor tree. Consider the following example:
The LCM of two numbers ( A & B) is 120 and the HCF is 4.
Step 1: find the prime factors of the LCM
i.e PF of LCM are 2 2 2 3 5
However note that the HCF of the numbers A & B is 4 and so we could re-write the PF of the LCM as 2 4 3 5
We now proceed as if we were finding the LCM of the two numbers but in reverse to produce several possible values of A & B (note the factor 4 appears in both columns as it is (highest) common factor.
Using prime factorisation method:
(i) 56 and 77
Factor of 56=2×2×2×7
Factor of 77=7×11
HCF (77,56)=7
LCM (56,7)=2×2×2×7×11=616