Have you ever wondered what the Least Common Multiple (LCM) of 10 and 14 is? It's 70. The LCM of two numbers is the smallest number that both numbers can divide into evenly. For example, the multiples of 10 (10, 20, 30, 40, 50, 60, etc.) and 14 (14, 28, 42, 56, etc.) share 70 as a common multiple. The LCM of 10 and 14 can be calculated using three different methods: division, prime factorization, and listing multiples.
The LCM of 10 and 14 is 70, and we will show you how to find this using various methods. The LCM of two non-zero integers, in this case 10 and 14, is the smallest positive integer (70) that is divisible by both numbers without leaving a remainder.
Methods to Calculate the LCM of 10 and 14
The LCM of 10 and 14 can be found using three different methods:
Prime Factorisation
Division method
Listing the multiples
Calculating the LCM of 10 and 14 Using Prime Factorisation
The prime factorisation of 10 and 14 are as follows:
10 = 2 1 × 5 1 and 14 = 2 1 × 7 1
Therefore, LCM (10, 14) = 70
Finding the LCM of 10 and 14 Using the Division Method
By dividing the numbers 10 and 14 by their common prime factors, we can find the LCM. The LCM is then found by multiplying these divisors.
2
10
14
5
5
7
7
1
7
1
1
So, LCM (10, 14) = 70
Listing the Multiples to Find the LCM of 10 and 14
To find the LCM of 10 and 14 by listing the multiples, we list the multiples of both numbers and find the smallest common multiple.
The LCM of 10 and 14 is 70. To find the least common multiple of 10 and 14, we need to find the multiples of 10 and 14 (multiples of 10 = 10, 20, 30, 40 . . . . 70; multiples of 14 = 14, 28, 42, 56 . . . . 70) and choose the smallest multiple that is exactly divisible by 10 and 14, i.e., 70.
Which of the following is the LCM of 10 and 14? 2, 45, 70, 27
The value of LCM of 10, 14 is the smallest common multiple of 10 and 14. The number satisfying the given condition is 70.
If the LCM of 14 and 10 is 70, Find its GCF.
LCM(14, 10) × GCF(14, 10) = 14 × 10. Since the LCM of 14 and 10 = 70, ⇒ 70 × GCF(14, 10) = 140. Therefore, the greatest common factor (GCF) = 140/70 = 2.