LCM of 40 and 100

LCM of 40 and 100 is the smallest number among all common multiples of 40 and 100. The first few multiples of 40 and 100 are (40, 80, 120, 160, 200, 240, 280, . . . ) and (100, 200, 300, 400, 500, . . . ) respectively. There are 3 commonly used methods to find LCM of 40 and 100 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 40 and 100 is 200.

Explanation:

The LCM of two non-zero integers, x(40) and y(100), is the smallest positive integer m(200) that is divisible by both x(40) and y(100) without any remainder.

The methods to find the LCM of 40 and 100 are explained below.

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

LCM of 40 and 100 by Prime Factorization

Prime factorization of 40 and 100 is (2 × 2 × 2 × 5) = 2³ × 5¹ and (2 × 2 × 5 × 5) = 2² × 5² respectively. LCM of 40 and 100 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 5² = 200.
Hence, the LCM of 40 and 100 by prime factorization is 200.

LCM of 40 and 100 by Listing Multiples

To calculate the LCM of 40 and 100 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 100 (100, 200, 300, 400, 500, . . . . )
• Step 2: The common multiples from the multiples of 40 and 100 are 200, 400, . . .
• Step 3: The smallest common multiple of 40 and 100 is 200.

∴ The least common multiple of 40 and 100 = 200.

LCM of 40 and 100 by Division Method

To calculate the LCM of 40 and 100 by the division method, we will divide the numbers(40, 100) by their prime factors (preferably common). The product of these divisors gives the LCM of 40 and 100.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 40 and 100. Write this prime number(2) on the left of the given numbers(40 and 100), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (40, 100) 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 100 is the product of all prime numbers on the left, i.e. LCM(40, 100) by division method = 2 × 2 × 2 × 5 × 5 = 200.

☛ Also Check:

• LCM of 3, 9 and 21 - 63
• LCM of 13 and 91 - 91
• LCM of 4, 7 and 14 - 28
• LCM of 4, 6 and 12 - 12
• LCM of 4, 6 and 10 - 60
• LCM of 50 and 75 - 150
• LCM of 12, 15, 20 and 27 - 540

FAQs on LCM of 40 and 100

What is the LCM of 40 and 100?

The LCM of 40 and 100 is 200. To find the least common multiple (LCM) of 40 and 100, we need to find the multiples of 40 and 100 (multiples of 40 = 40, 80, 120, 160 . . . . 200; multiples of 100 = 100, 200, 300, 400) and choose the smallest multiple that is exactly divisible by 40 and 100, i.e., 200.

What is the Least Perfect Square Divisible by 40 and 100?

The least number divisible by 40 and 100 = LCM(40, 100)
LCM of 40 and 100 = 2 × 2 × 2 × 5 × 5 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 40 and 100 = LCM(40, 100) × 2 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.

Which of the following is the LCM of 40 and 100? 28, 18, 200, 36

The value of LCM of 40, 100 is the smallest common multiple of 40 and 100. The number satisfying the given condition is 200.

What is the Relation Between GCF and LCM of 40, 100?

The following equation can be used to express the relation between GCF and LCM of 40 and 100, i.e. GCF × LCM = 40 × 100.

If the LCM of 100 and 40 is 200, Find its GCF.

LCM(100, 40) × GCF(100, 40) = 100 × 40
Since the LCM of 100 and 40 = 200
⇒ 200 × GCF(100, 40) = 4000
Therefore, the greatest common factor (GCF) = 4000/200 = 20.