LCM of 30 and 40 is the smallest number among all common multiples of 30 and 40. The first few multiples of 30 and 40 are (30, 60, 90, 120, 150, 180, 210, . . . ) and (40, 80, 120, 160, 200, . . . ) respectively. There are 3 commonly used methods to find LCM of 30 and 40 - by prime factorization, by listing multiples, and by division method.

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1.LCM of 30 and 40
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 30 and 40 is 120.

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Explanation:

The LCM of two non-zero integers, x(30) and y(40), is the smallest positive integer m(120) that is divisible by both x(30) and y(40) without any remainder.


The methods to find the LCM of 30 and 40 are explained below.

By Division MethodBy Prime Factorization MethodBy Listing Multiples

LCM of 30 and 40 by Division Method

To calculate the LCM of 30 and 40 by the division method, we will divide the numbers(30, 40) by their prime factors (preferably common). The product of these divisors gives the LCM of 30 and 40.

Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 30 and 40 is the product of all prime numbers on the left, i.e. LCM(30, 40) by division method = 2 × 2 × 2 × 3 × 5 = 120.

LCM of 30 and 40 by Prime Factorization

Prime factorization of 30 and 40 is (2 × 3 × 5) = 21 × 31 × 51 and (2 × 2 × 2 × 5) = 23 × 51 respectively. LCM of 30 and 40 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 31 × 51 = 120.Hence, the LCM of 30 and 40 by prime factorization is 120.

LCM of 30 and 40 by Listing Multiples

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To calculate the LCM of 30 and 40 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 30 (30, 60, 90, 120, 150, 180, 210, . . . ) and 40 (40, 80, 120, 160, 200, . . . . )Step 2: The common multiples from the multiples of 30 and 40 are 120, 240, . . .Step 3: The smallest common multiple of 30 and 40 is 120.

∴ The least common multiple of 30 and 40 = 120.

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FAQs on LCM of 30 and 40

What is the LCM of 30 and 40?

The LCM of 30 and 40 is 120. To find the least common multiple (LCM) of 30 and 40, we need to find the multiples of 30 and 40 (multiples of 30 = 30, 60, 90, 120; multiples of 40 = 40, 80, 120, 160) and choose the smallest multiple that is exactly divisible by 30 and 40, i.e., 120.

What is the Relation Between GCF and LCM of 30, 40?

The following equation can be used to express the relation between GCF and LCM of 30 and 40, i.e. GCF × LCM = 30 × 40.

What is the Least Perfect Square Divisible by 30 and 40?

The least number divisible by 30 and 40 = LCM(30, 40)LCM of 30 and 40 = 2 × 2 × 2 × 3 × 5 ⇒ Least perfect square divisible by each 30 and 40 = LCM(30, 40) × 2 × 3 × 5 = 3600 Therefore, 3600 is the required number.

What are the Methods to Find LCM of 30 and 40?

The commonly used methods to find the LCM of 30 and 40 are:

Division MethodListing MultiplesPrime Factorization Method

If the LCM of 40 and 30 is 120, Find its GCF.

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LCM(40, 30) × GCF(40, 30) = 40 × 30Since the LCM of 40 and 30 = 120⇒ 120 × GCF(40, 30) = 1200Therefore, the GCF (greatest common factor) = 1200/120 = 10.