LCM Of 5,7 and 10

The LCM of 5,7 and 10 is 70. But how did we get to this answer? This is what we will be learning. Let us also look at the different ways by which we can find the LCM of 2 or more numbers.

As we have read before, there are different ways to find the LCM of 2 or more numbers. Here, is a list of those methods which make it easy to find the LCMs:

• Listing Of Multiples

• Prime Factorization

• Division Method

Let us look deeper into these three methods and how it helps us.
 

In this simple method, we will list all the multiples of 5,7 and 10. Then we will try to find a multiple that is present in all 3 numbers.

For example, 

Multiple of 5:  5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100

Multiple of 7:  7,114,21,28,35,42,49,56,63,70,77,84,91,98,105.

Multiple of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

As highlighted, 70 is the lowest multiple that is common in 5,7 and 10. So, 70 is the LCM of 5,7 and 10.
 

Let us break down the given numbers into smaller numbers using only prime numbers. So, 5 will be written as 5, 7 will be written as 7 and 10 will be written as (5x2). We can see that 5 appears twice in the list of numbers. So, we will consider this only once. Now, the list is like 2,5 and 7. 

Now, we have to multiply these numbers to get the least common multiple. 

2x5x7=70. 

We get the answer of 70. This is the least common multiple or the LCM of 5,7 and 10.
 

To calculate the LCM using this method is very simple. We will divide the given numbers by their prime factors. The product of these divisors will give us the LCM of the given numbers.

Let us understand it step by step:

Step 1: First, find the lowest prime factor that can divide at least one of the numbers. In this case, the lowest prime factor is 2. And it divides 10, which will give us a quotient of 5.

Step 2: Now, the numbers that remain are two 5s and one 7. Since these two numbers are prime numbers, it can’t be divisible by any other number. So, now the lowest number is 5. Divide the possible numbers by 5. This will leave only a 7 in the table.

Step 3: Now, divide the 7 by 7. This will only 1s in the last row of the table. Now, on the left side we can see the numbers 2,5 and 7. 

Step 4: Multiply these numbers, and we will get the answer as 70 (7×5×2=70). The answer, 70 is the LCM of 5,7 and 10.

• Prime Numbers- Any number that has only 2 factors is called a prime number.For example, 2 and 3. Both these numbers have only 2 factors,1 and the number itself.

• Prime Factorization- Breaking off big numbers into smaller numbers using prime numbers.For example, 10 can be broken down as 5×2, where 5 and 2 are prime numbers.

• Divisible-  It means for a number to divide another number and leave no remainder.For example, 10/5 where the quotient will be 2 and the remainder will be 0.