LCM of 40 and 48

LCM of 40 and 48 is the smallest number among all common multiples of 40 and 48. The first few multiples of 40 and 48 are (40, 80, 120, 160, 200, 240, 280, . . . ) and (48, 96, 144, 192, 240, 288, . . . ) respectively. There are 3 commonly used methods to find LCM of 40 and 48 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 40 and 48 is 240.

Explanation:

The LCM of two non-zero integers, x(40) and y(48), is the smallest positive integer m(240) that is divisible by both x(40) and y(48) without any remainder.

The methods to find the LCM of 40 and 48 are explained below.

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

LCM of 40 and 48 by Listing Multiples

To calculate the LCM of 40 and 48 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, 200, 240, 280, . . . ) and 48 (48, 96, 144, 192, 240, 288, . . . . )
• Step 2: The common multiples from the multiples of 40 and 48 are 240, 480, . . .
• Step 3: The smallest common multiple of 40 and 48 is 240.

∴ The least common multiple of 40 and 48 = 240.

LCM of 40 and 48 by Prime Factorization

Prime factorization of 40 and 48 is (2 × 2 × 2 × 5) = 2³ × 5¹ and (2 × 2 × 2 × 2 × 3) = 2⁴ × 3¹ respectively. LCM of 40 and 48 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ × 5¹ = 240.
Hence, the LCM of 40 and 48 by prime factorization is 240.

LCM of 40 and 48 by Division Method

To calculate the LCM of 40 and 48 by the division method, we will divide the numbers(40, 48) by their prime factors (preferably common). The product of these divisors gives the LCM of 40 and 48.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 40 and 48. Write this prime number(2) on the left of the given numbers(40 and 48), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (40, 48) 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 48 is the product of all prime numbers on the left, i.e. LCM(40, 48) by division method = 2 × 2 × 2 × 2 × 3 × 5 = 240.

☛ Also Check:

• LCM of 16 and 48 - 48
• LCM of 15 and 27 - 135
• LCM of 7 and 35 - 35
• LCM of 4, 8, 12 and 24 - 24
• LCM of 17 and 5 - 85
• LCM of 14 and 15 - 210
• LCM of 22 and 55 - 110

FAQs on LCM of 40 and 48

What is the LCM of 40 and 48?

The LCM of 40 and 48 is 240. To find the least common multiple of 40 and 48, we need to find the multiples of 40 and 48 (multiples of 40 = 40, 80, 120, 160 . . . . 240; multiples of 48 = 48, 96, 144, 192 . . . . 240) and choose the smallest multiple that is exactly divisible by 40 and 48, i.e., 240.

What is the Relation Between GCF and LCM of 40, 48?

The following equation can be used to express the relation between GCF and LCM of 40 and 48, i.e. GCF × LCM = 40 × 48.

What is the Least Perfect Square Divisible by 40 and 48?

The least number divisible by 40 and 48 = LCM(40, 48)
LCM of 40 and 48 = 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 40 and 48 = LCM(40, 48) × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

If the LCM of 48 and 40 is 240, Find its GCF.

LCM(48, 40) × GCF(48, 40) = 48 × 40
Since the LCM of 48 and 40 = 240
⇒ 240 × GCF(48, 40) = 1920
Therefore, the greatest common factor (GCF) = 1920/240 = 8.

How to Find the LCM of 40 and 48 by Prime Factorization?

To find the LCM of 40 and 48 using prime factorization, we will find the prime factors, (40 = 2 × 2 × 2 × 5) and (48 = 2 × 2 × 2 × 2 × 3). LCM of 40 and 48 is the product of prime factors raised to their respective highest exponent among the numbers 40 and 48.
⇒ LCM of 40, 48 = 2⁴ × 3¹ × 5¹ = 240.