Multiples and factors (prime factorization)

Advanced Math 5 · Unit 3 · prime-factorization-gcf-lcm · Teacher edition

prime-factorization-gcf-lcm

Name ______________________________Date ______________

1.
Write $72$ as a product of primes in index notation. What is the exponent of $2$ ?
Answer: ______________
2.
Using $24 = 2^3 \cdot 3$ and $90 = 2 \cdot 3^2 \cdot 5$ , find $\text{LCM}(24, 90)$ .
Answer: ______________
3.
A red light flashes every $8$ seconds and a blue light flashes every $12$ seconds. They flash together now. In how many seconds will they next flash together?
1. (A)
  $4$
2. (B)
  $48$
3. (C)
  $96$
4. (D)
  $24$

Answer key — Multiples and factors (prime factorization)

1.
3prime-factorization-gcf-lcm-01
$72 = 8 \times 9 = (2 \times 2 \times 2) \times (3 \times 3) = 2^3 \times 3^2$ . The exponent of $2$ is $\mathbf{3}$ .
2.
360prime-factorization-gcf-lcm-02
$\text{LCM} = 2^3 \cdot 3^2 \cdot 5 = 8 \times 9 \times 5 = \mathbf{360}$ . Check: $\text{GCF}(24, 90) = 2 \cdot 3 = 6$ , and $6 \times 360 = 2{,}160 = 24 \times 90$ . ✓
3.
(D)
$24$
prime-factorization-gcf-lcm-03
$\text{LCM}(8, 12) = 2^3 \cdot 3 = \mathbf{24}$ seconds. ( $4$ is the GCF; $96 = 8 \times 12$ is a common multiple but not the least — it counts the shared $2^2$ twice; $48 = 2^4 \cdot 3$ has one $2$ too many.)