Correct option is B
Given:
We need to find which pair can be HCF and LCM of two numbers
Options:
A) 21, 372
B) 38, 342
C) 488, 62
D) 124, 4
A) 21, 372
B) 38, 342
C) 488, 62
D) 124, 4
Formula Used:
HCF × LCM = Product of two numbers
LCM must be divisible by HCF
LCM ≥ HCF (always)
Solution:
Option A: (21, 372)
Check divisibility:
372 ÷ 21 = 17.71 (not an integer)
372 ÷ 21 = 17.71 (not an integer)
So, not possible
Option B: (38, 342)
Check divisibility:
342 ÷ 38 = 9
342 ÷ 38 = 9
Let numbers be:
a = 38x, b = 38y
a = 38x, b = 38y
Then LCM = 38xy = 342
=> xy = 9 (possible)
=> xy = 9 (possible)
So, valid
Option C: (488, 62)
Here:
LCM = 62, HCF = 488
LCM = 62, HCF = 488
But:
62 < 488
62 < 488
LCM is always greater than or equal to HCF
So, not possible
Option D: (124, 4)
Here:
LCM = 4, HCF = 124
LCM = 4, HCF = 124
Again:
4 < 124
4 < 124
Violates rule
So, not possible
Final Answer:
Only option B (38, 342) is correct
The correct option is (B)
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