LCM of 30 72 and 432

LCM of 30, 72 and 432 is 2160. LCM stands for least common multiple in Mathematics. The least common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. The article HCF and LCM is prepared by a team of experts who have vast knowledge in Maths. Students can make use of this article to learn the simple process of calculating HCF and LCM of given numbers with ease. Let us learn how to verify the least common multiple of 30, 72 and 432 using solved examples and FAQs in this article.

What is LCM of 30, 72 and 432?

The Least Common Multiple of 30, 72 and 432 is 2160.

How to Find LCM of 30, 72 and 432?

The LCM of 30, 72 and 432 can be determined by using three methods:

• Prime Factorisation
• Division method
• Listing the Multiples

LCM of 30, 72 and 432 Using Prime Factorisation Method

In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 30, 72 and 432 can be expressed as;

30 = 2 × 3 × 5

72 = 2 × 2 × 2 × 3 × 3

432 = 2 × 2 × 2 × 2 × 3 × 3 × 3

LCM (30, 72, 432) = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2160

LCM of 30, 72 and 432 Using Division Method

In the division method, we divide the numbers 30, 72 and 432 by their prime factors until we get the result as one in the complete row. The product of these divisors gives the least common multiple of 30, 72 and 432.

No further division can be done.

Therefore, LCM (30, 72, 432) = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2160

LCM of 30, 72 and 432 Using Listing the Multiples

Here, we list down the multiples of given natural numbers to find the lowest common multiple among them. The multiples of 30, 72 and 432 are as follows:

Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, ………, 2100, 2130, 2160, ……

Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720, ………, 2016, 2088, 2160, …..

Multiples of 432: 432, 864, 1296, 1728, 2160, ……….

LCM (30, 72, 432) = 2160

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Solved Examples

1. What is the smallest number that is divisible by 30, 72, 432 exactly?

Solution: The lowest common multiple of 30, 72 and 432 will be the smallest number that is divisible by 30, 72, 432 exactly. The LCM of 30, 72 and 432 is 2160. Therefore, the smallest number that is divisible by 30, 72 and 432 exactly is 2160. 

2. What are the first five multiples of 30, 72 and 432?

Solution: The first five multiples of 30, 72 and 432 are as follows:

Multiples of 30 = 30, 60, 90, 120, and 150

Multiples of 72 = 72, 144, 216, 288, and 360

Multiples of 432 = 432, 864, 1296, 1728, and 2160