Question:
Three numbers are in the ratio 4:5:7 and their LCM is 5040. Their HCF is:
Three numbers are in the ratio 4:5:7 and their LCM is 5040. Their HCF is:
Updated On: Sep 16, 2026
- 28
- 32
- 35
- 36
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The Correct Option is D
Solution and Explanation
Concept:
Step 1: Write the three numbers using a common factor k
Ratio = 4 : 5 : 7, so the numbers = 4k, 5k, 7k
Step 2: Find the LCM of the three numbers in terms of k
Since 4, 5 and 7 share no common factor with each other, LCM of 4k, 5k, 7k = 4 x 5 x 7 x k = 140k
Step 3: Use the given LCM to solve for k
140k = 5040
k = 5040/140 = 36
Step 4: State the HCF
Since 4, 5, 7 share no common factor, the HCF of 4k, 5k, 7k is simply k
HCF = 36
Final Answer: 36
- When numbers are given in a ratio whose terms share no common factor among themselves, the HCF of the actual numbers equals the common multiplying factor k.
- The LCM of numbers in ratio a:b:c (with a, b, c having no common factor pairwise) equals a x b x c x k.
- Use the given LCM to find k, which directly gives the HCF.
Step 1: Write the three numbers using a common factor k
Ratio = 4 : 5 : 7, so the numbers = 4k, 5k, 7k
Step 2: Find the LCM of the three numbers in terms of k
Since 4, 5 and 7 share no common factor with each other, LCM of 4k, 5k, 7k = 4 x 5 x 7 x k = 140k
Step 3: Use the given LCM to solve for k
140k = 5040
k = 5040/140 = 36
Step 4: State the HCF
Since 4, 5, 7 share no common factor, the HCF of 4k, 5k, 7k is simply k
HCF = 36
Final Answer: 36
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