LCM of 5, 6 and 7 is 210. LCM is the shortform for Least Common Multiple/Lowest Common Multiple. It is also termed as the LCD which stands for Least Common Divisor. LCM/LCD is the positive integer that is a common multiple of the given group of numbers. Here the given set of numbers are 5, 6 and 7. The smallest common multiple for all these numbers among many is 210, and hence it is the LCM. You can refer to LCM for all details.
What is LCM of 5, 6 and 7
The Least Common Multiple or Lowest Common Multiple of 5, 6 and 7 is 210.
How to Find LCM of 5, 6 and 7?
LCM of 5, 6 and 7 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 5, 6 and 7 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 5, 6 and 7 can be expressed as;
5 = 1 × 5
6 = 2 × 3
7 = 1 × 7
Since 5 and 7 are the prime numbers, both 5 and 7 are multiplied by the prime factors of 6 to get the LCM.
Therefore, LCM (5, 6 and 7) = 2 × 3 × 5 × 7 = 210
LCM of 5, 6 and 7 Using Division Method
In the Division Method, the numbers 5,6, 7 are divided by the smallest prime divisors. Since 5 and 7 are both prime, they are 2 divisors. 6 will be divisible by 2 and 3 as prime factors. Therefore LCM will be the product of all these prime divisors.
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LCM (5, 6 and 7) = 2 × 3 × 5 × 7 = 210
LCM of 5, 6 and 7 Using Listing the Multiples
By listing all the multiples of 5, 6 and 7, we can identify the LCM. Below is the list of multiples for 5, 6 and 7
Multiples of 5
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220
Multiples of 6
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222
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
LCM (5, 6 and 7) = 210
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 5, 6 and 7?
Answer: 210 is the smallest number that is divisible by 5, 6 and 7.
What is the LCM of 2, 3, 5, 6 and 7?
Answer: LCM of 2, 3, 5, 6 and 7 is 210 as 2 and 3 is the factor for 6.
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