Final answer:
To find the least common multiple (LCM), list the multiples of each number and find the smallest multiple that appears in both lists. The LCM is the smallest multiple that two or more numbers have in common.
Step-by-step explanation:
The least common multiple (LCM) is the smallest multiple that two or more numbers have in common. To find the LCM, you can start by listing the multiples of each number and then look for the smallest multiple that appears in each list.
a. For 4 and 9, the multiples are: 4, 8, 12, 16, 20, 24, 28, 32, 36... and 9, 18, 27, 36, 45, 54, 63, 72, 81... The smallest multiple that appears in both lists is 36, so LCM(4, 9) = 36.
b. For 8 and 64, the multiples are: 8, 16, 24, 32, 40, 48, 56, 64... and 64, 128, 192, 256, 320, 384, 448, 512... The smallest multiple that appears in both lists is 64, so LCM(8, 64) = 64.
c. For 14 and 19, the multiples are: 14, 28, 42, 56, 70, 84, 98... and 19, 38, 57, 76, 95, 114, 133... The smallest multiple that appears in both lists is 266, so LCM(14, 19) = 266.
d. For 36 and 48, the multiples are: 36, 72, 108, 144, 180, 216, 252, 288, 324... and 48, 96, 144, 192, 240, 288, 336, 384, 432... The smallest multiple that appears in both lists is 144, so LCM(36, 48) = 144.
e. For 100 and 70, the multiples are: 100, 200, 300, 400, 500, 600, 700... and 70, 140, 210, 280, 350, 420, 490... The smallest multiple that appears in both lists is 700, so LCM(100, 70) = 700.