Discovering the LCM of 12, 24, and 36 unveils the number 72. In the world of mathematics, the Least Common Multiple (LCM) of any two or more numbers is the smallest number that is divisible by all the given numbers. The LCM of 12, 24, and 36, therefore, is the smallest common multiple of these numbers. There are various methods to calculate the LCM, including prime factorization, division, and listing multiples.
For further reading: What is the Least Common Multiple?
The LCM of 12, 24, and 36 is 72. This article provides a detailed explanation of how to calculate the LCM of these numbers using various methods. The LCM of any two non-zero integers is the smallest positive integer that is divisible by both numbers without leaving a remainder.
There are three primary methods to find the LCM of 12, 24, and 36:
The prime factorisation of 12, 24, and 36 are as follows:
12 = 2² x 3
24 = 2³ x 3
36 = 2² x 3²
Therefore, the LCM of 12, 24, and 36 is 72.
In the division method, we divide the numbers 12, 24, and 36 by their common prime factors. The LCM is then calculated by multiplying these divisors.
After performing the division, we find that the LCM of 12, 24, and 36 is 72.
To find the LCM by listing multiples, we list the multiples of 12, 24, and 36. The smallest common multiple of these numbers is 72.
Therefore, the LCM of 12, 24, and 36 is 72.
Let's find the smallest number that is divisible by 12, 24, and 36.
Solution:
The smallest number that is divisible by 12, 24, and 36 is their LCM.
So, the LCM of 12, 24, and 36 is 72.
What is the LCM of 12, 24 and 36?
The LCM of 12, 24, and 36 is 72. To find the LCM (least common multiple) of 12, 24, and 36, we need to find the multiples of 12, 24, and 36 (multiples of 12 = 12, 24, 36, 48, 72 . . . .; multiples of 24 = 24, 48, 72, 96 . . . .; multiples of 36 = 36, 72, 108, 144 . . . .) and choose the smallest multiple that is exactly divisible by 12, 24, and 36, i.e., 72.
List the methods used to find the LCM of 12, 24 and 36.
The methods used to find the LCM of 12, 24 and 36 are Prime Factorization Method, Division Method and Listing multiples.
Which of the following is the LCM of 12, 24, and 36? 72, 3, 24, 10
The value of LCM of 12, 24, 36 is the smallest common multiple of 12, 24, and 36. The number satisfying the given condition is 72.
What is the Relation Between GCF and LCM of 12, 24, 36?
The following equation can be used to express the relation between GCF and LCM of 12, 24, 36, i.e. LCM(12, 24, 36) = [(12 × 24 × 36) × GCF(12, 24, 36)]/[GCF(12, 24) × GCF(24, 36) × GCF(12, 36)].