which pairs of numbers have an lcm of 24? choose all that apply. 3 and 8 2 and 12 6 and 4 8 and 6 4 and 12
which pairs of numbers have an lcm of 24? choose all that apply. 3 and 8 2 and 12 6 and 4 8 and 6 4 and 12
Answer
Explanation:
Step1: Recall LCM formula
The least - common multiple (LCM) of two non - zero integers (a) and (b) can be found by prime - factorizing the numbers and then taking the highest power of each prime factor.
Step2: Prime - factorize numbers for 3 and 8
Prime - factorize (3=3^1) and (8 = 2^3). Then (LCM(3,8)=3\times2^3=24).
Step3: Prime - factorize numbers for 2 and 12
Prime - factorize (2 = 2^1) and (12=2^2\times3^1). Then (LCM(2,12)=2^2\times3^1 = 12).
Step4: Prime - factorize numbers for 6 and 4
Prime - factorize (6 = 2^1\times3^1) and (4=2^2). Then (LCM(6,4)=2^2\times3^1=12).
Step5: Prime - factorize numbers for 8 and 6
Prime - factorize (8 = 2^3) and (6=2^1\times3^1). Then (LCM(8,6)=2^3\times3^1 = 24).
Step6: Prime - factorize numbers for 4 and 12
Prime - factorize (4 = 2^2) and (12=2^2\times3^1). Then (LCM(4,12)=2^2\times3^1=12).
Answer:
A. 3 and 8, D. 8 and 6