22 is the H.C.F of two numbers. The LCM of these two numbers has factors 12…
2025
22 is the H.C.F of two numbers. The LCM of these two numbers has factors 12 and 13. Which is larger of the two numbers?
- A.
456
- B.
286
- C.
765
- D.
234
Show answer & explanation
Correct answer: B
When two numbers have HCF H, and the co-prime factors of their LCM (with respect to H) are m and n, the two numbers are H × m and H × n.
HCF = 22; the co-prime factors of the LCM are 12 and 13.
First number = 22 × 12 = 264.
Second number = 22 × 13 = 286.
Check: HCF(264, 286) = 22 since 264 = 22 × 12, 286 = 22 × 13, and 12, 13 are co-prime (no common factor other than 1).
Since 286 > 264, the larger of the two numbers is 286.