HCF and LCM Interview Questions
If the ratio of two numbers is 3:5 and their HCF is 4, what is the LCM? — spoken sample answer for Indian interviews.
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If the ratio of two numbers is 3:5 and their HCF is 4, what is the LCM?
If the ratio is 3:5 and HCF is 4, the numbers are 3 times 4 and 5 times 4, which is 12 and 20. For two numbers, LCM times HCF equals the product, so LCM is (12 times 20) / 4 = 60. I can also say LCM of 3x and 5x is 15x, and x is 4, so 60. I would mark 60.
HCF 12, LCM 240, one number 48. Other number?
Product equals HCF times LCM. 48x=2880, x=60. I check HCF(48,60)=12. The check catches arithmetic mistakes.
Three numbers, HCF 5, LCM 300. Can you find them uniquely?
No. I need a ratio or another constraint. I would not invent 5, 10, 300 without checking. Blind formulas fail uniqueness.
LCM of 12 and 18 with primes?
12=2^2*3, 18=2*3^2. LCM max powers 36. HCF min powers 6. Prime powers scale to three numbers. I would not list multiples when numbers are large.
Ratio 3:5, LCM 75. Find the numbers.
3x and 5x, LCM 15x=75, x=5, numbers 15 and 25. I check HCF and LCM. If the ratio is not coprime I reduce it first.
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