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Home > Pre-Algebra calculators > LCM by Prime Factorization Method example
6. LCM by Prime Factorization Method example ( Enter your problem )
( Enter your problem )
  1. Examples
 		Other related methods
  1. HCF by Listing Method
  2. HCF by Prime Factorization Method
  3. HCF by Division Method
  4. HCF by Repeated Division Method
  5. LCM by Listing Method
  6. LCM by Prime Factorization Method
  7. LCM by Division Method
  8. LCD
  9. Common Factor by Listing Method
5. LCM by Listing Method
(Previous method)		7. LCM by Division Method
(Next method)

1. Examples


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

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

230
315
55
 1
 
240
220
210
55
 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

345
315
55
 1
 
525
55
 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
  
225
  
55
 
120
  
260
  
230
  
215
  
35

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
  
2200
  
2100
  
250
  
225
  
55
 
140
  
270
  
235
  
57

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

230
315
55
 1
 
240
220
210
55
 1
 
250
525
55
 1
 
260
230
315
55
 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`

This material is intended as a summary. Use your textbook for detail explanation.
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5. LCM by Listing Method
(Previous method)		7. LCM by Division Method
(Next method)


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