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The LCM of two numbers is seven times of their HCF. If the product of two numbers is 448, then find the difference between LCM and HCF.
48
54
42
30
48
Since LCM×HCF=7×HCF2=448, calculate HCF2=448/7=64. Then HCF=8, so LCM=7×8=56. The difference is 56−8=48.
The LCM of two numbers is 7 times their HCF. The product of these two numbers is 448.
LCM×HCF=Product of two numbers, LCM=7×HCF
Since LCM×HCF=7×HCF2=448, calculate HCF2=448/7=64. Then HCF=8, so LCM=7×8=56. The difference is 56−8=48.
Many students mistake the relationship LCM=7×HCF as LCM+HCF=7 or divide the product by 7 without considering the squared term (HCF2).
Define Relationship
Let HCF be x. Then LCM is 7x. Given the product of two numbers is 448.
LCM×HCF=448
Solve for HCF
Substitute LCM=7x and HCF=x into the product formula: (7x)×(x)=448.
7x2=448⟹x2=64⟹x=8
Calculate LCM and Difference
Since HCF=8, calculate LCM=7×8=56. The difference is LCM−HCF=56−8=48.
56−8=48
A is correct because the calculated HCF is 8 and LCM is 56, resulting in a difference of 48.
This concept frequently appears in 'Number Systems' and 'Algebraic Identities' questions where variables are linked by fixed ratios.
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