LCM of 30 and 40

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.

Answer: LCM of 30 and 40 is 120.

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 Method
• By Prime Factorization Method
• By 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 1: Find the smallest prime number that is a factor of at least one of the numbers, 30 and 40. Write this prime number(2) on the left of the given numbers(30 and 40), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (30, 40) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
• 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

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.

☛ Also Check:

• LCM of 3, 5 and 7 - 105
• LCM of 25 and 65 - 325
• LCM of 8, 12 and 18 - 72
• LCM of 21 and 27 - 189
• LCM of 12, 16, 24 and 36 - 144
• LCM of 3, 4 and 9 - 36
• LCM of 5, 6, 7 and 8 - 840

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 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 30 and 40 = LCM(30, 40) × 2 × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
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 Method
• Listing Multiples
• Prime Factorization Method

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

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