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The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F.?
- a)12
- b)8
- c)35
- d)24
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The L.C.M. of three different numbers is 120. Which of the following c...
LCM = 2 × 2 × 2 × 3 × 5
Hence, HCF = 4, 8, 12 or 24
According to question
35 cannot be H.C.F. of 120.
Hence, HCF = 4, 8, 12 or 24
According to question
35 cannot be H.C.F. of 120.
Most Upvoted Answer
The L.C.M. of three different numbers is 120. Which of the following c...
Understanding L.C.M. and H.C.F.
The relationship between the Least Common Multiple (L.C.M.) and the Highest Common Factor (H.C.F.) of three numbers can be expressed as:
Product of Numbers = L.C.M. × H.C.F.
In this case, the L.C.M. of the three different numbers is 120.
Exploring H.C.F. Values
To find the possible H.C.F.s, we can rearrange the formula:
H.C.F. = Product of Numbers / L.C.M.
This indicates that the H.C.F. must be a divisor of the L.C.M. (120).
Divisors of 120
The divisors of 120 are:
Analyzing Options for H.C.F.
Now, let’s evaluate the given options for H.C.F.:
Conclusion
Since H.C.F. must divide the L.C.M., the value **35** cannot be the H.C.F. of three numbers whose L.C.M. is 120. Thus, the correct answer is option **C**.
The relationship between the Least Common Multiple (L.C.M.) and the Highest Common Factor (H.C.F.) of three numbers can be expressed as:
Product of Numbers = L.C.M. × H.C.F.
In this case, the L.C.M. of the three different numbers is 120.
Exploring H.C.F. Values
To find the possible H.C.F.s, we can rearrange the formula:
H.C.F. = Product of Numbers / L.C.M.
This indicates that the H.C.F. must be a divisor of the L.C.M. (120).
Divisors of 120
The divisors of 120 are:
- 1
- 2
- 3
- 4
- 5
- 6
- 8
- 10
- 12
- 15
- 20
- 24
- 30
- 40
- 60
- 120
Analyzing Options for H.C.F.
Now, let’s evaluate the given options for H.C.F.:
- 12: Valid (12 × 10 = 120 with numbers like 12, 20, 30)
- 8: Valid (8 × 15 = 120 with numbers like 8, 15, 40)
- 35: Invalid (35 is not a divisor of 120)
- 24: Valid (24 × 5 = 120 with numbers like 24, 30, 40)
Conclusion
Since H.C.F. must divide the L.C.M., the value **35** cannot be the H.C.F. of three numbers whose L.C.M. is 120. Thus, the correct answer is option **C**.
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