Exercise 544Number theory › PrimesHigh schoolAdded 3 Nov 2026

GCD and LCM via prime factorization

#gcd#lcm#prime factorization

Statement

Write $\gcd$ and $\operatorname{lcm}$ of $a=2^4\cdot3^2\cdot5$ and $b=2^2\cdot3^3\cdot7$ in terms of prime factorization.

Hint

Min exponents for gcd, max for lcm.

Show solutionHide solution

GCD. $2^2\cdot3^2=4\cdot9=36$ .

LCM. $2^4\cdot3^3\cdot5\cdot7=16\cdot27\cdot35=15120$ .

Check. $\gcd\cdot\operatorname{lcm}=36\cdot15120=544320$ , $ab=720\cdot756=544320$ . ✓

Conclusion. $\gcd=36$ , $\operatorname{lcm}=15120$ .