GCD and LCM of 168 and 576

Statement

Compute the GCD and the LCM of $168$ and $576$.

Solution

One factorises the two numbers into primes; then the GCD takes the common factors with the smaller exponent, the LCM all the factors with the larger exponent: $\begin{aligned} 168 &= 2^3\cdot 3\cdot 7 \\ 576 &= 2^6\cdot 3^2 \\[4pt] \text{MCD} &= 2^3\cdot 3 = \boxed{24} \\ \text{mcm} &= 2^6\cdot 3^2\cdot 7 = \boxed{4032} \end{aligned}$

Links

Topics: Numbers and operations
Concepts: Prime factorisation · Greatest common divisor (GCD) · Least common multiple (LCM)
Skills: Factorise
Exercise type: Factorisation