Question

What is the LCM of 80,45 and 35 by using the division method

Answer 1

Starting with

80, 45, 35

divide each number by the first prime number, 2, as many times as needed until you arrive at 1. If it's not perfectly divisible by 2, leave it alone.

40, 45, 35 … … … 1 division by 2

20, 45, 35 … … … 2 divisions

10, 45, 35 … … … 3 divisions

5, 45, 35 … … … 4 divisions

We stop here, and take note that we divided by 2⁴.

Now continue with the next prime, 3.

5, 15, 35 … … … 1 division by 3

5, 5, 35 … … … 2 divisions

Stop; we've divided by 3².

Now with the next prime, 5.

1, 1, 7 … … … 1 division by 5

Stop; we've divided by 5¹.

The next prime is 7.

1, 1, 1 … … … 1 division by 7

Stop; we've divided by 7¹.

The division method then says that the LCM of 80, 45, and 35 is then

2⁴ × 3² × 5¹ × 7¹ = 16 × 9 × 5 × 7 = 5040