Assertion: For any two positive integers a and b. HCF (a, b) x LCM (a,b) = ax b Reason: The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.
Answers
Step-by-step explanation:
If 150 is a multiple, then all of the factors of the second number must also be factors of 150 which are: 5 (twice), 2 and 3.
Since 150 is the LCM, all of those factors must be either in our number or 25. Since 25 has just 5 (twice) as a factor, both 2 and 3 must be factors.
The remaining question is how many 5s we have. Since the GCF with 25 is 5, our number must exactly one 5.
So the factors of our number are: 2, 3, and 5. There is one number with exactly these factors = 2*3*5 = 30.
Given : Assertion: For any two positive integers a and b. HCF (a, b) x LCM (a,b) = ax b
Reason: The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.
To Find : Comment on Assertion and reason
Solution:
Assertion: For any two positive integers a and b. HCF (a, b) x LCM (a,b) = ax b
LCM * HCF of two numbers = Product of two numbers
Hence Assertion is TRUE
Reason: The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.
LCM = 150/5 = 30
30 ≠ 40
Hence Reason is False
Assertion is TRUE and Reason is False
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