The HCF of two numbers is 12 and their LCM is 336. If one number is 48, what is the other?
The other number is 84. For any two numbers, HCF x LCM = product of the numbers, so the other number is 12 x 336 / 48 = 84.
Explain it simply
Each number is the HCF multiplied by its own private part. Here 48 = 12 x 4. The LCM collects the shared part once and every private part once. Multiplying HCF and LCM therefore gives back exactly the same pieces as multiplying the two numbers. That identity only holds for two numbers, not three.
Example
Question: HCF = 12, LCM = 336, one number = 48. Find the other.
- HCF x LCM = first x second.
- 12 x 336 = 4032.
- Other number = 4032 / 48 = 84.
Check: 48 = 12 x 4 and 84 = 12 x 7. Since 4 and 7 share no factor, HCF = 12 and LCM = 12 x 4 x 7 = 336. Both match.
console.log((12 * 336) / 48); // Output: 84What to say in the interview
"For two numbers, HCF times LCM equals their product. So the other number is 12 times 336 divided by 48, which is 84. I check by writing both as 12 times a co-prime pair, 4 and 7."
Common mistakes
- Applying HCF x LCM = product to three numbers; it is not true in general there.
- Not checking the answer: a set of values where the LCM is not a multiple of the HCF has no solution, and examiners sometimes test that.