How many times larger is the least common multiple of 96 and 160 than the greatest common factor of 96 and 160?

The least common multiple (LCM) of two integers is the smallest positive integer that is a multiple of both
The greatest common Factor (GCF) of two integers is the largest positive integer dividing both
Ex: 12 is the least common multiple of 4 and 6 and 2 is the greatest common factor of them

∵ The multiples of 96 are

96 × 1 = 96, 96 × 2 = 192, 96 × 3 = 288, 96 × 4 = 384, 96 × 5 = 480, ....

∵ The multiples of 160 are

160 × 1 = 160, 160 × 2 = 320, 160 × 3 = 480, 160 × 4 = 640, ....

∵ The first common multiple of them is 480

∴ The least common multiple of 96 and 160 is 480

∵ 96 = 1 × 96 , 2 × 48 , 3 × 32 , 4 × 24 , 6 × 16 , 8 × 12

∴ The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

∵ 160 = 1 × 160 , 2 × 80 , 4 × 40 , 5 × 32 , 8 × 20 , 10 × 16

∴ The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160

- Find the common factors of them

∵ The common factors of them are 1, 2, 4, 8, 16, 32

∵ The greatest one is 32

∴ The greatest common factor of 96 and 160 is 32

∵ LCM = 480

∵ GCF = 32

∵ 480 ÷ 32 = 15

∴ The LCM is 15 times larger than the GCF of 96 and 160

The least common multiple of 96 and 160 is 15 times larger than the greatest common factor of 96 and 160

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peaceandlovesike peaceandlovesike · Answer 2 · 2020-10-19T21:03:40+02:00

Answer:

its 15

Step-by-step explanation:

math :)

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