What is lcm 135,225,45 ?

The solution to lcm 135,225,45 is 675

Find the LCM 135 , 225 , 45

lcm

675

Solution steps

135, 225, 45

Prime factorization of

135 : 3 \cdot 3 \cdot 3 \cdot 5

135

135

divides by

3135 = 45 \cdot 3

= 3 \cdot 45

45

divides by

345 = 15 \cdot 3

= 3 \cdot 3 \cdot 15

15

divides by

315 = 5 \cdot 3

= 3 \cdot 3 \cdot 3 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 3 \cdot 3 \cdot 5

Prime factorization of

225 : 3 \cdot 3 \cdot 5 \cdot 5

225

225

divides by

3225 = 75 \cdot 3

= 3 \cdot 75

75

divides by

375 = 25 \cdot 3

= 3 \cdot 3 \cdot 25

25

divides by

525 = 5 \cdot 5

= 3 \cdot 3 \cdot 5 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 3 \cdot 5 \cdot 5

Prime factorization of

45 : 3 \cdot 3 \cdot 5

45

45

divides by

345 = 15 \cdot 3

= 3 \cdot 15

15

divides by

315 = 5 \cdot 3

= 3 \cdot 3 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 3 \cdot 5

Compute a number comprised of factors that appear in at least one of the following:

135, 225, 45

= 3 \cdot 3 \cdot 3 \cdot 5 \cdot 5

Multiply the numbers:

3 \cdot 3 \cdot 3 \cdot 5 \cdot 5 = 675

= 675