LCM of 150 and 500 is 1500. The Least/Lowest Common multiple(LCM) is the smallest number such that when divided by the given numbers, the division is complete. In the given set of numbers 150 and 500, 1500 is the first(least or smallest) number that is common in the set of multiples of 150 and 500. 3000 is also the common multiple of 150 and 500. However, 1500 is the smallest. Hence 1500 is the LCM which is also known as LCD, Least Common Divisor for 150 and 500. You can read more on LCM for further details.
What is the LCM of 150 and 500?
The Least Common Multiple or Lowest Common Multiple of 150 and 500 is 1500.
How to Find LCM of 150 and 500?
LCM of 150 and 500 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 150 and 500 Using Prime Factorisation Method
In the Prime Factorisation method, 150 and 500 can be expressed as;
150 = 2 × 3 × 5 × 5
500 = 2 × 2 × 5 × 5 × 5
Factors 2, 5, 5 are common and factors 2, 3, 5 are not common. Multiplying both common and uncommon numbers forms the LCM.
LCM (150, 500) = 2 × 2 × 3 × 5 × 5 × 5 = 1500
LCM of 150 and 500 Using Division Method
In the Division Method for 150 and 500, both are divided by prime divisors starting with 2 and till the remainders are one. Only prime divisors are used for division. The product of all the prime divisors forms the LCM.
|
2 |
150 |
500 |
|
2 |
75 |
250 |
|
3 |
75 |
125 |
|
5 |
25 |
125 |
|
5 |
5 |
25 |
|
5 |
1 |
5 |
|
× |
1 |
1 |
LCM (150, 500) = 2 × 2 × 3 × 5 × 5 × 5 = 1500
LCM of 150 and 500 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the smallest common multiple, which is the LCM. Below is the list of multiples for 150 and 500
|
Multiples of 150 |
Multiples of 500 |
|
150 |
500 |
|
300 |
1000 |
|
450 |
1500 |
|
600 |
2000 |
|
750 |
2500 |
|
900 |
3000 |
|
1050 |
3500 |
|
1200 |
4000 |
|
1350 |
4500 |
|
1500 |
5000 |
LCM (150, 500) = 1500
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 150 and 500?
Answer: 1500 is the smallest number that is divisible by both 150 and 500.
What is the LCM for 15, 150 and 500?
Answer: LCM for 15, 150 and 500 is 1500 as 15 is the factor of 150.
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