Question

What’s the least common multiple (LCM) for each group of numbers? a. 6 and 15 b. 4 and 11 c. 6, 9, and 12 d. 8, 10, and 20 What’s the least common denominator (LCD) for each group of fractions? a. 1⁄6 and 7⁄8 b. 3⁄4 and 7⁄10 c. 7⁄12, 3⁄8 and 11⁄36 d. 8⁄15, 11⁄30 and 3⁄5

Answer 1

LCM
a. 30
b. 44
c. 36
d. 40


LCD
a. 24
b. 20
c. 72
d. 30

Answer 2

LCM is least common multiple.

a. 6 and 15

6 = 2 x 3

15 = 3 x 5

LCM = 3 x 5 x 2 = 30

b. 4 and 11

4 = 2 x 2

11 = 1 x 11

LCM = 2 x 2 x 11 = 44

c. 6, 9, and 12

6 = 2 x 3

9 = 3 x 3

12 = 2 x 2 x 3

LCM = 2 x 2 x 3 x 3 = 36

d. 8, 10, and 20

8 = 2 x 2 x 2

10 = 2 x 5

20 = 2 x 2 x 5

LCM = 2 x 2 x 2 x 5 = 40

LCD is the least common denominator. Means we will find the LCM of denominators.

a. 1⁄6 and 7⁄8

6 = 2 x 3

8 = 2 x 2 x 2

LCD = 2 x 2 x 2 x 3 = 24

b. 3⁄4 and 7⁄10

4 = 2 x 2

10 = 2 x 5

LCD = 2 x 2 x 5 = 20

c. 7⁄12, 3⁄8 and 11⁄36

12 = 2 x 2 x 3

8 = 2 x 2 x 2

36 = 2 x 2 x 3 x 3

LCD = 2 x 2 x 2 x 3 x 3 = 72

d. 8⁄15, 11⁄30 and 3⁄5

15 = 3 x 5

30 = 2 x 3 x 5

5 = 1 x 5

LCD = 2 x 3 x 5 = 30