LCM of 40, 56, and 60

LCM of 40, 56, and 60 is the smallest number among all common multiples of 40, 56, and 60. The first few multiples of 40, 56, and 60 are (40, 80, 120, 160, 200 . . .), (56, 112, 168, 224, 280 . . .), and (60, 120, 180, 240, 300 . . .) respectively. There are 3 commonly used methods to find LCM of 40, 56, 60 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 40, 56, and 60 is 840.

Explanation:

The LCM of three non-zero integers, a(40), b(56), and c(60), is the smallest positive integer m(840) that is divisible by a(40), b(56), and c(60) without any remainder.

The methods to find the LCM of 40, 56, and 60 are explained below.

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

LCM of 40, 56, and 60 by Prime Factorization

Prime factorization of 40, 56, and 60 is (2 × 2 × 2 × 5) = 2³ × 5¹, (2 × 2 × 2 × 7) = 2³ × 7¹, and (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ respectively. LCM of 40, 56, and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 5¹ × 7¹ = 840.
Hence, the LCM of 40, 56, and 60 by prime factorization is 840.

LCM of 40, 56, and 60 by Division Method

To calculate the LCM of 40, 56, and 60 by the division method, we will divide the numbers(40, 56, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 40, 56, and 60.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 40, 56, and 60. Write this prime number(2) on the left of the given numbers(40, 56, and 60), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (40, 56, 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, 56, and 60 is the product of all prime numbers on the left, i.e. LCM(40, 56, 60) by division method = 2 × 2 × 2 × 3 × 5 × 7 = 840.

LCM of 40, 56, and 60 by Listing Multiples

To calculate the LCM of 40, 56, 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, 200 . . .), 56 (56, 112, 168, 224, 280 . . .), and 60 (60, 120, 180, 240, 300 . . .).
• Step 2: The common multiples from the multiples of 40, 56, and 60 are 840, 1680, . . .
• Step 3: The smallest common multiple of 40, 56, and 60 is 840.

∴ The least common multiple of 40, 56, and 60 = 840.

☛ Also Check:

• LCM of 18 and 27 - 54
• LCM of 2, 3, 4 and 5 - 60
• LCM of 4, 5 and 10 - 20
• LCM of 6, 15 and 18 - 90
• LCM of 20, 25 and 30 - 300
• LCM of 12, 14 and 16 - 336
• LCM of 8, 12 and 24 - 24

FAQs on LCM of 40, 56, and 60

What is the LCM of 40, 56, and 60?

The LCM of 40, 56, and 60 is 840. To find the LCM of 40, 56, and 60, we need to find the multiples of 40, 56, and 60 (multiples of 40 = 40, 80, 120, 160 . . . . 840 . . . . ; multiples of 56 = 56, 112, 168, 224 . . . . 840 . . . . ; multiples of 60 = 60, 120, 180, 240 . . . . 840 . . . . ) and choose the smallest multiple that is exactly divisible by 40, 56, and 60, i.e., 840.

What are the Methods to Find LCM of 40, 56, 60?

The commonly used methods to find the LCM of 40, 56, 60 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

Which of the following is the LCM of 40, 56, and 60? 35, 2, 52, 840

The value of LCM of 40, 56, 60 is the smallest common multiple of 40, 56, and 60. The number satisfying the given condition is 840.

How to Find the LCM of 40, 56, and 60 by Prime Factorization?

To find the LCM of 40, 56, and 60 using prime factorization, we will find the prime factors, (40 = 2³ × 5¹), (56 = 2³ × 7¹), and (60 = 2² × 3¹ × 5¹). LCM of 40, 56, and 60 is the product of prime factors raised to their respective highest exponent among the numbers 40, 56, and 60.
⇒ LCM of 40, 56, 60 = 2³ × 3¹ × 5¹ × 7¹ = 840.