Exercise 457Number theory › Divisibility and gcdHigh schoolAdded 3 Nov 2026

LCM of three numbers

#lcm#three numbers#prime factorization

Statement

Compute $\operatorname{lcm}(12,18,30)$ .

Hint

Prime factorization: take the largest exponent of each prime.

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Factorizations.
$12=2^2\cdot3,\qquad 18=2\cdot3^2,\qquad 30=2\cdot3\cdot5.$

LCM. Largest exponent of each prime: $2^2\cdot3^2\cdot5=4\cdot9\cdot5=180$ .

Conclusion. $\operatorname{lcm}(12,18,30)=180$ .

Check. $180=15\cdot12=10\cdot18=6\cdot30$ . Correct.