LCM of 3, 7 and 10 is 210. LCM is the short form for Least/Lowest Common Multiple. LCM also referred to as LCD (Least Common Divisor) is a common multiple for two or more numbers that is also the smallest. Here the given set of numbers are 3, 7 and 10. The smallest common multiple for all these numbers among many is 210, and hence it is the LCM. You can refer to LCM with Examples to understand better.
What is LCM of 3, 7 and 10
The Least Common Multiple or Lowest Common Multiple of 3, 7 and 10 is 210.
How to Find LCM of 3, 7 and 10?
LCM of 3, 7 and 10 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 7 and 10 Using Prime Factorisation Method
In the Prime Factorisation method for 3, 7 and 10, only 10 can be expressed as the product of prime factors. 3 and 7 are both prime numbers. Hence LCM will be a product of all the prime factors.
3 = 1 × 3
7 = 1 × 7
10 = 2 × 5
LCM(3, 7 and 10) = 2 × 3 × 7 × 5 = 210
LCM of 3, 7 and 10 Using Division Method
In the Division Method for 3, 7 and 10, only 1 is the common factor. Here 10 is divided with the smallest divisor which is 2. We are left with 3 prime numbers 3, 5, and 7 along with the divisor 2. The product of these numbers gives us the LCM.
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LCM(3, 7 and 10) = 2 × 3 × 5 × 7 = 210
LCM of 3, 7 and 10 Using Listing the Multiples
By listing all the multiples of given numbers, we can look for the smallest common multiple, which is the LCM. Below is the list of multiples for 3, 7 and 10. 210 is the first common multiple for 3, 7 and 10.
Multiples of 3
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, 198, 201, 204, 207, 210, 213, 216
Multiples of 7
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224
Multiples of 10
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230
LCM(3, 7 and 10) = 210
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 3, 7 and 10?
Answer: 210 is the smallest number that is divisible by 3, 7 and 10.
What is the LCM of 3, 7 and 210?
Answer: LCM of 3, 7 and 210 is 210.
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