find the hcf and lcm of 350 and 400 and verify that hcf×lcm = product of two product
Answers
350=2*5*5*7
400=2*2*2*2*5*5
therefore
hcf =50
and lcm=2800.
now
lcm *hcf =products of number
50*2800=350*400
140000=140000.
hence verified.
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Concept: In mathematics, Least Common Multiple is referred to by its entire name, whereas Highest Common Factor is its complete name. The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the H.C.F. describes the biggest factor existing between any given pair of two or more numbers. LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).
Given: the numbers 350 and 400
To find: the HCF and LCM
Solution: The prime factors of 350 and 400 are:
350 = 2 × 5 × 5 × 7
400 = 2 × 2 × 2 × 2 × 5 × 5
Therefore, the highest common factor (HCF) = 2 × 5 × 5 = 50
Now for finding the LCM,
the prime factors for 350 and 400 are 2 × 2 × 2 × 2 × 5 × 5 × 7 = 2800
Therefore, the least common factor (LCM) of 350 and 400 is 2800.
Verification:
HCF × LCM = product of two numbers
50 × 2800 = 350 × 400
140000 = 140000
Hence verified.
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