LCM of 6, 7 and 9 is 126. LCM is abbreviated as Least Common multiple or Lowest common multiple. LCM is the simplest method to find out the smallest common multiples between two or more than two numbers.
The LCM of 6,7 and 9 is 126.
What is the LCM of 6, 7 and 9?
The Least Common Multiple or Lowest Common Multiple of 6, 7 and 9 is 126.
How to Find LCM of 6, 7 and 9?
Regularly we use three different methods for finding the LCM of 6, 7 and 9. They are
- By Prime Factorisation
- By Division method
- By Listing the multiples
LCM of 6, 7 and 9 Using Prime Factorisation Method
Prime factorization of 6, 7 and 9 are (2 × 3) = 21× 31 and ( 7 ) = 71 and (3 × 3) = 32, respectively .
LCM of 6, 7 and 9 can be obtained by multiplying prime factors raised to their respective highest power.
i.e., 21 × 32× 71 = 126.
Hence, the LCM of 6, 7 and 9 by prime factorization is 126.
LCM of 6,7 and 9 by Division Method
To calculate the LCM of 6, 7 and 9 by the division method, we will divide the numbers 6, 7 and 9 by their prime factors. The product of these divisors gives the LCM of 6, 7 and 9.
Let us see the steps to follow:
Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6, 7 and 9.
Step 2: If any of the given numbers 6, 7 or 9 is a multiple of 2, divide it by 2 and write the quotient below it. Bring down the number as it is, if it is not divisible by the prime number
Step 3: Continue these steps until you get only 1’s in the last row.
The LCM of 6, 7 and 9 by division method is 126.
| 2 | 6 | 7 | 9 |
| 3 | 3 | 7 | 9 |
| 3 | 1 | 7 | 3 |
| 7 | 1 | 7 | 1 |
| 1 | 1 | 1 |
Hence the LCM of 6,7 and 9 = 2 × 3 × 3 × 7 = 126
LCM of 6,7 and 9 by Listing Multiples
To calculate the LCM of 6, 7 and 9, list the multiples of 6, 7 and 9.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63,….
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …
Step 1: List out a few multiples of 6,7 and 9.
Step 2: Now the common multiples from the multiples of 6,7 and 9 are 126, 252, …
Step 3: The smallest common multiple of 6, 7 and 9 is 126.
Hence, the least common multiple of 6, 7 and 9 = 126.
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Solved Example
Example:
Find the smallest number that is divisible by 6, 7 and 9 exactly.
Solution:
The smallest number that is divisible by 6, 7 and 9 exactly is their LCM.
Therefore, the LCM of 6, 7 and 9 is 126.
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