LCM of 10 and 70 is 70. LCM is abbreviated as Least Common multiple or Lowest common multiple. Usually, this is written as LCM(10, 70)=70.
LCM is the simplest method to find out the smallest common multiples between two or more than two numbers.
The LCM of 10 and 70, is the smallest number among all the common multiples of 10 and 70.
What is the LCM of 10 and 70?
The Least Common Multiple or Lowest Common Multiple of 10 and 70 is 70.
How to Find LCM of 10 and 70?
Let us see the different methods for finding the LCM of 10 and 70. The three commonly used methods are:
- By Prime Factorisation
- By Division method
- By Listing the multiples
LCM of 10 and 70 Using Prime Factorisation Method
Step 1: Find the prime factorization of 10.
10 = 2 × 5
Step 2: Find the prime factorization of 70.
70 = 2 × 5 × 7
Step 3: Multiply each factor the greater number of times.
Step 4: 2 × 5 × 7 = 70
LCM of 10 and 70 by Division Method
To calculate the LCM of 10 and 70 by the division method, we will divide the numbers 10 and 70 by their prime factors. The product of these divisors gives the LCM of 10 and 70.
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, 10 and 70.
Step 2: If any of the given numbers 10 or 70 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 10 and 70 by division method is 70.
| 2 | 10 | 70 |
| 5 | 5 | 35 |
| 7 | 1 | 7 |
| 1 | 1 |
LCM= 2 × 5 × 7 = 70
LCM of 10 and 70 by Listing Multiples
To calculate the LCM of 10 and 70, list the multiples of 10 and 70.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, …
Multiples of 70: 70, 140, …
Step 1: List out a few multiples of 10 and 70.
Step 2: Now the common multiples from the multiples of 10 and 70 are 70, 140, …
Step 3: The smallest common multiple of 10 and 70 is 70.
Hence the least common multiple of 10 and 70 = 70.
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Solved Example
Example:
What is the smallest number that is divisible by 10 and 70 exactly?
Solution:
The smallest number that is divisible by 10 and 70 exactly is their LCM.
Therefore, the LCM of 10 and 70 is 70.
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