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Question
If HCF(98, 28) = m and LCM(98, 28) = n, then the value of n - 7m is ______.
Options
0
28
98
196
MCQ
Fill in the Blanks
Solution
If HCF(98, 28) = m and LCM(98, 28) = n, then the value of n - 7m is 98.
Explanation:
Step 1: Find HCF (98, 28)
The highest common factor (HCF) is the greatest number that divides both 98 and 28.
Prime factorisation:
98 = 2 × 7 × 7
28 = 2 × 2 × 7
Common factors: 2 and 7
HCF = 2 × 7 = 14
m = 14
Step 2: Find LCM (98,28)
The least common multiple (LCM) is found using the formula:
LCM (a, b) = `(a ×b)/("HCF" (a,b))`
LCM( 98,28) = `(98 × 28)/14 = 2744/14 = 196`
n = 196
Step 3: Compute n − 7m
= n − 7m = 196 − (7×14)
= 196 − 98
= 98
The value of n − 7m is 98.
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