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The ratio between HCF and LCM of two numbers 62 and 217 is 1 : 14. Find the LCM.
439
402
430
434
434
Let HCF=x and LCM=14x. Using the property HCF├ЧLCM=a├Чb, we get x├Ч14x=62├Ч217. Since HCF must be a common factor of 62, we check divisors of 62 (1, 2, 31, 62). Testing x=31 satisfies the equation.
Two numbers are 62 and 217. The ratio of their HCF to LCM is 1 : 14.
LCM├ЧHCF=a├Чb
Let HCF=x and LCM=14x. Using the property HCF├ЧLCM=a├Чb, we get x├Ч14x=62├Ч217. Since HCF must be a common factor of 62, we check divisors of 62 (1, 2, 31, 62). Testing x=31 satisfies the equation.
Students often confuse the product of HCF and LCM with the sum or fail to link the given ratio constant directly to the numbers' prime factorization.
Define variables
Let HCF = x and LCM = 14x based on the given ratio 1:14.
HCF=x,LCM=14x
Apply Product Formula
The product of two numbers equals the product of their HCF and LCM: x├Ч14x=62├Ч217.
14x2=62├Ч217
Calculate x (HCF)
Divide by 14 and solve for x2: x2=(62├Ч217)/14=(62├Ч31)/2=31├Ч31. So, x=31.
x2=312тЯ╣x=31
Find LCM
Since LCM = 14x, substitute x=31 into the expression.
LCM=14├Ч31=434
D is correct because the product of the numbers 62├Ч217 is 13454, and 14x2=13454 gives x=31, leading to LCM=14├Ч31=434.
This concept is a classic in Number Systems; always remember the identity Product=HCF├ЧLCM for two numbers, as it is a frequent source of marks in SSC/Railways exams.
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