LCM by Prime Factorization Method calculator

SolutionHelp

Solution

Solution provided by AtoZmath.com

1. Find LCM of 30,40 using Prime Factorization Method

Solution:
Step-1: Prime factorization of `30,40` using factor by division method

2	30
3	15
5	5
	1

2	40
2	20
2	10
5	5
	1

Step-2: Write each number as a product of primes, matching primes vertically when possible

30	=	2			× 3	× 5
40	=	2	× 2	× 2		× 5

Step-3: Bring down the primes in each column. The LCM is the product of these factors

30	=	2			× 3	× 5
40	=	2	× 2	× 2		× 5

LCM	=	2	× 2	× 2	× 3	× 5	= 120

`:.` LCM of `30,40` is `120`

2. Find LCM of 45,25 using Prime Factorization Method

Solution:
Step-1: Prime factorization of `45,25` using factor by division method

3	45
3	15
5	5
	1

5	25
5	5
	1

Step-2: Write each number as a product of primes, matching primes vertically when possible

45	=	3	× 3	× 5
25	=			5	× 5

Step-3: Bring down the primes in each column. The LCM is the product of these factors

45	=	3	× 3	× 5
25	=			5	× 5

LCM	=	3	× 3	× 5	× 5	= 225

`:.` LCM of `45,25` is `225`

3. Find LCM of 50,120 using Prime Factorization Method

Solution:
Step-1: Prime factorization of `50,120` using factor tree method

	50

2		25

	5		5

	120

2		60

	2		30

		2		15

			3		5

Step-2: Write each number as a product of primes, matching primes vertically when possible

50	=	2				× 5	× 5
120	=	2	× 2	× 2	× 3	× 5

Step-3: Bring down the primes in each column. The LCM is the product of these factors

50	=	2				× 5	× 5
120	=	2	× 2	× 2	× 3	× 5

LCM	=	2	× 2	× 2	× 3	× 5	× 5	= 600

`:.` LCM of `50,120` is `600`

4. Find LCM of 400,140 using Prime Factorization Method

Solution:
Step-1: Prime factorization of `400,140` using factor tree method

	400

2		200

	2		100

		2		50

			2		25

				5		5

	140

2		70

	2		35

		5		7

Step-2: Write each number as a product of primes, matching primes vertically when possible

400	=	2	× 2	× 2	× 2	× 5	× 5
140	=	2	× 2			× 5		× 7

Step-3: Bring down the primes in each column. The LCM is the product of these factors

400	=	2	× 2	× 2	× 2	× 5	× 5
140	=	2	× 2			× 5		× 7

LCM	=	2	× 2	× 2	× 2	× 5	× 5	× 7	= 2800

`:.` LCM of `400,140` is `2800`

5. Find LCM of 30,40,50,60 using Prime Factorization Method

Solution:
Step-1: Prime factorization of `30,40,50,60` using factor by division method

2	30
3	15
5	5
	1

2	40
2	20
2	10
5	5
	1

2	50
5	25
5	5
	1

2	60
2	30
3	15
5	5
	1

Step-2: Write each number as a product of primes, matching primes vertically when possible

30	=	2			× 3	× 5
40	=	2	× 2	× 2		× 5
50	=	2				× 5	× 5
60	=	2	× 2		× 3	× 5

Step-3: Bring down the primes in each column. The LCM is the product of these factors

30	=	2			× 3	× 5
40	=	2	× 2	× 2		× 5
50	=	2				× 5	× 5
60	=	2	× 2		× 3	× 5

LCM	=	2	× 2	× 2	× 3	× 5	× 5	= 600

`:.` LCM of `30,40,50,60` is `600`