Two numbers are in the ratio 3:4 and their H.C.F. is 4. Find their L.C.M.

Given data

• Numbers = 3h and 4h with H.C.F. = h = 4.

Concept / Approach

• When ratio terms are coprime (3 and 4), LCM(3h, 4h) = 12h.
• Alternatively: product = (H.C.F.) × (L.C.M.).

Step-by-step computation

h = 4 ⇒ numbers are 12 and 16.LCM(12, 16) = 2^2 × 3 × 2^4/2^2? Or directly = (12 × 16) / HCF(12,16) = (192)/4 = 48.

Verification

Multiples: 12 → 12,24,36,48; 16 → 16,32,48 ⇒ first common is 48.

Common pitfalls

• Assuming H.C.F. is 1 for 3:4; remember the actual numbers share factor h.

Final Answer

L.C.M. = 48.