Subjective Type

Find the LCM and HCF of the following pair of integers and verify that LCM * HCF = product of two numbers: $$902$$ and $$1517$$.

Solution

Given numbers are $$902$$ and $$1517$$
The prime factorization of $$902$$ and $$1517$$ gives:
$$902=2*11*41$$ and $$1517=37*41$$
Therefore, the HCF of these two integers = $$41$$
Now, the LCM of $$902$$ and $$1517=2*11*37*41=33374$$
Now, we have to verify,
[LCM $$(a,b)$$ * HCF $$(a,b)$$ = product of two numbers $$(a*b)$$]
LHS = LCM * HCF = $$33374*41=1368334$$
RHS = Product of two numbers = $$902*1517=1368334$$
Hence, LHS=RHS
So, the product of two numbers is equal to the product of their HCF and LCM.

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