4, 6, 12, 15 का लघुत्तम समापवर्तक (L.C.M.) = ?

Question

4, 6, 12, 15 का लघुत्तम समापवर्तक (L.C.M.) = ?

1. A. 180
2. B. 60 (Correct answer)
3. C. 72
4. D. 120

Correct Answer

Option B — 60

Detailed Solution & Explanation

The correct answer is 60.

Key Points

• Prime factorise: 4 = 2², 6 = 2×3, 12 = 2²×3, 15 = 3×5.
• LCM = highest power of each prime = 2² × 3 × 5 = 60.

Exam Tip

• Verify by division: 60 ÷ 4 = 15, ÷ 6 = 10, ÷ 12 = 5, ÷ 15 = 4 — all exact, and no smaller option works.

Additional Information

• For any two numbers, LCM × HCF = product of the numbers — a relation asked directly almost every year. (It does not extend to three or more numbers.)
• HCF takes the *lowest* power of each common prime; LCM takes the *highest* power of every prime present.
• The LCM is always a multiple of each number and the HCF always a factor — so the LCM can never be smaller than the largest number given.