LCM of 40 and 60

LCM of 40 and 60 is the smallest number among all common multiples of 40 and 60. The first few multiples of 40 and 60 are (40, 80, 120, 160, . . . ) and (60, 120, 180, 240, . . . ) respectively. There are 3 commonly used methods to find LCM of 40 and 60 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 40 and 60 is 120.

Explanation:

The LCM of two non-zero integers, x(40) and y(60), is the smallest positive integer m(120) that is divisible by both x(40) and y(60) without any remainder.

The methods to find the LCM of 40 and 60 are explained below.

• By Listing Multiples
• By Prime Factorization Method
• By Division Method

LCM of 40 and 60 by Listing Multiples

To calculate the LCM of 40 and 60 by listing out the common multiples, we can follow the given below steps:

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

∴ The least common multiple of 40 and 60 = 120.

LCM of 40 and 60 by Prime Factorization

Prime factorization of 40 and 60 is (2 × 2 × 2 × 5) = 2³ × 5¹ and (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ respectively. LCM of 40 and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 5¹ = 120.
Hence, the LCM of 40 and 60 by prime factorization is 120.

LCM of 40 and 60 by Division Method

To calculate the LCM of 40 and 60 by the division method, we will divide the numbers(40, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 40 and 60.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 40 and 60. Write this prime number(2) on the left of the given numbers(40 and 60), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (40, 60) 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 40 and 60 is the product of all prime numbers on the left, i.e. LCM(40, 60) by division method = 2 × 2 × 2 × 3 × 5 = 120.

☛ Also Check:

• LCM of 18 and 20 - 180
• LCM of 3, 4 and 5 - 60
• LCM of 36, 48 and 72 - 144
• LCM of 56 and 84 - 168
• LCM of 12, 45 and 75 - 900
• LCM of 12, 15 and 21 - 420
• LCM of 21 and 30 - 210

FAQs on LCM of 40 and 60

What is the LCM of 40 and 60?

The LCM of 40 and 60 is 120. To find the least common multiple (LCM) of 40 and 60, we need to find the multiples of 40 and 60 (multiples of 40 = 40, 80, 120, 160; multiples of 60 = 60, 120, 180, 240) and choose the smallest multiple that is exactly divisible by 40 and 60, i.e., 120.

What is the Relation Between GCF and LCM of 40, 60?

The following equation can be used to express the relation between GCF and LCM of 40 and 60, i.e. GCF × LCM = 40 × 60.

What are the Methods to Find LCM of 40 and 60?

The commonly used methods to find the LCM of 40 and 60 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

What is the Least Perfect Square Divisible by 40 and 60?

The least number divisible by 40 and 60 = LCM(40, 60)
LCM of 40 and 60 = 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 40 and 60 = LCM(40, 60) × 2 × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

If the LCM of 60 and 40 is 120, Find its GCF.

LCM(60, 40) × GCF(60, 40) = 60 × 40
Since the LCM of 60 and 40 = 120
⇒ 120 × GCF(60, 40) = 2400
Therefore, the greatest common factor (GCF) = 2400/120 = 20.