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The HCF and LCM of two numbers are 6 and 1824, respectively. If one number is 96, then the other number is:
112
114
216
192
114
Use the property that the product of two numbers is equal to the product of their HCF and LCM. Divide the HCF by 6 (or simplify the fraction) and solve for the unknown.
HCF = 6, LCM = 1824, one number = 96.
HCF×LCM=Number1×Number2
Use the property that the product of two numbers is equal to the product of their HCF and LCM. Divide the HCF by 6 (or simplify the fraction) and solve for the unknown.
Many students try to find the prime factorization of 1824 instead of simply using the product formula.
State the relationship
For any two numbers, the product of the numbers equals the product of their HCF and LCM.
HCF×LCM=Number1×Number2
Substitute the given values
Plug in the given values: HCF = 6, LCM = 1824, and one number = 96 into the equation.
6×1824=96×Number2
Solve for the second number
Isolate the second number: Number2=966×1824. Simplifying 966=161, then calculating 1824/16=114.
114=9610944
B is correct because the product of HCF and LCM (10944) divided by the given number (96) equals 114.
This formula Product=HCF×LCM is fundamental and frequently tested in competitive exams like RRB, SSC, and Banking.
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