The Least Common Multiple (LCM) of 10 and 30 is 30. The LCM is the smallest number that both 10 and 30 can divide into evenly. The initial multiples of 10 are (10, 20, 30, 40, 50, 60, 70, . . .) and for 30, they are (30, 60, 90, 120, . . .). In Mathematics, the LCM of any pair of numbers is a value that can be evenly divided by both of these numbers. Various methods can be employed to find the LCM, such as prime factorisation, division, and listing multiples.
The LCM of 10 and 30 is 30. This article illustrates various methods to find the LCM of 10 and 30. The LCM of the non-zero integers 10 and 30 is the smallest positive integer, 30, that can be divided by both 10 and 30 without leaving a remainder.
Methods to Find the LCM of 10 and 30
The LCM of 10 and 30 can be determined using three different methods:
Prime Factorisation
Division Method
Listing the Multiples
Finding the LCM of 10 and 30 Using Prime Factorisation
The prime factorisation of 10 and 30, respectively, yields:
10 = 21 x 51
30 = 21 x 31 x 51
The LCM of 10 and 30 is therefore 30.
Finding the LCM of 10 and 30 Using the Division Method
By dividing the numbers 10 and 30 by their common prime factors, we can find the LCM using the division method. The LCM of 10 and 30 is the product of these divisors.
2
10
30
5
5
15
3
1
3
x
1
1
No further division is possible.
Thus, the LCM of 10 and 30 is 30.
Finding the LCM of 10 and 30 by Listing the Multiples
To find the LCM of 10 and 30 by listing the common multiples, write out the multiples as shown below:
The LCM of 10 and 30 is 30. To find the LCM (least common multiple) of 10 and 30, we need to find the multiples of 10 and 30 (multiples of 10 = 10, 20, 30, 40; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 10 and 30, i.e., 30.
Which of the following is the LCM of 10 and 30? 40, 5, 28, 30
The value of LCM of 10, 30 is the smallest common multiple of 10 and 30. The number satisfying the given condition is 30.
If the LCM of 30 and 10 is 30, Find its GCF.
LCM(30, 10) × GCF(30, 10) = 30 × 10. Since the LCM of 30 and 10 = 30, ⇒ 30 × GCF(30, 10) = 300. Therefore, the greatest common factor (GCF) = 300/30 = 10.