The least common multiple (LCM) of 25 and 30 is 150 . In mathematics, the LCM of two integers is the smallest number that both numbers can divide evenly. Hence, the LCM of 25 and 30 is the smallest multiple that both 25 and 30 can divide evenly. Some of the first few multiples of 25 and 30 include (25, 50, 75, 100, 150, etc.) and (30, 60, 90, 120, 150, etc.). There are three common methods to find the LCM of 25 and 30: prime factorization, listing multiples, and division.
The LCM of 25 and 30 is 150. This article will explain how to find the LCM of these two non-zero integers using various methods. The smallest positive integer that both 25 and 30 can divide evenly without leaving a remainder is 150.
UGC NET/SET Course Online by SuperTeachers: Complete Study Material, Live Classes & More
You can find the LCM of 25 and 30 using three methods:
Prime Factorisation
Division method
Listing the multiples
Finding the LCM of 25 and 30 Using the Prime Factorisation Method
The prime factorisation of 25 and 30 is as follows:
25 = (5 × 5) = 5 2 and
30 = (2 × 3 × 5) = 2 1 × 3 1 × 5 1
LCM (25, 30) = 150
Finding the LCM of 25 and 30 Using the Division Method
To find the LCM of 25 and 30 using the division method, divide the numbers (25, 30) by their common prime factors. The LCM of 25 and 30 is the product of these divisors.
Hence, LCM (25, 30) = 150
Finding the LCM of 25 and 30 by Listing the Multiples
To find the LCM of 25 and 30 by listing the multiples, start by listing the multiples of each number as shown below:
The smallest multiple that both 25 and 30 can divide evenly is 150.
The LCM of 25 and 30 is 150. To find the least common multiple of 25 and 30, we need to find the multiples of 25 and 30 and choose the smallest multiple that is exactly divisible by 25 and 30, i.e., 150.
If the LCM of 30 and 25 is 150, Find its GCF.
LCM(30, 25) × GCF(30, 25) = 30 × 25. Since the LCM of 30 and 25 = 150, ⇒ 150 × GCF(30, 25) = 750. Therefore, the greatest common factor = 750/150 = 5.
What is the Relation Between GCF and LCM of 25, 30?
The following equation can be used to express the relation between GCF and LCM of 25 and 30, i.e. GCF × LCM = 25 × 30.