LCM of 40 and 70

LCM of 40 and 70 is the smallest number among all common multiples of 40 and 70. The first few multiples of 40 and 70 are (40, 80, 120, 160, 200, 240, . . . ) and (70, 140, 210, 280, 350, 420, 490, . . . ) respectively. There are 3 commonly used methods to find LCM of 40 and 70 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 40 and 70 is 280.

Explanation:

The LCM of two non-zero integers, x(40) and y(70), is the smallest positive integer m(280) that is divisible by both x(40) and y(70) without any remainder.

The methods to find the LCM of 40 and 70 are explained below.

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

LCM of 40 and 70 by Prime Factorization

Prime factorization of 40 and 70 is (2 × 2 × 2 × 5) = 2³ × 5¹ and (2 × 5 × 7) = 2¹ × 5¹ × 7¹ respectively. LCM of 40 and 70 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 5¹ × 7¹ = 280.
Hence, the LCM of 40 and 70 by prime factorization is 280.

LCM of 40 and 70 by Listing Multiples

To calculate the LCM of 40 and 70 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, . . . ) and 70 (70, 140, 210, 280, 350, 420, 490, . . . . )
• Step 2: The common multiples from the multiples of 40 and 70 are 280, 560, . . .
• Step 3: The smallest common multiple of 40 and 70 is 280.

∴ The least common multiple of 40 and 70 = 280.

LCM of 40 and 70 by Division Method

To calculate the LCM of 40 and 70 by the division method, we will divide the numbers(40, 70) by their prime factors (preferably common). The product of these divisors gives the LCM of 40 and 70.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 40 and 70. Write this prime number(2) on the left of the given numbers(40 and 70), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (40, 70) 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 70 is the product of all prime numbers on the left, i.e. LCM(40, 70) by division method = 2 × 2 × 2 × 5 × 7 = 280.

☛ Also Check:

• LCM of 4 and 12 - 12
• LCM of 13 and 17 - 221
• LCM of 20 and 24 - 120
• LCM of 15 and 18 - 90
• LCM of 3 and 9 - 9
• LCM of 56 and 70 - 280
• LCM of 15 and 35 - 105

FAQs on LCM of 40 and 70

What is the LCM of 40 and 70?

The LCM of 40 and 70 is 280. To find the LCM of 40 and 70, we need to find the multiples of 40 and 70 (multiples of 40 = 40, 80, 120, 160 . . . . 280; multiples of 70 = 70, 140, 210, 280) and choose the smallest multiple that is exactly divisible by 40 and 70, i.e., 280.

What are the Methods to Find LCM of 40 and 70?

The commonly used methods to find the LCM of 40 and 70 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

How to Find the LCM of 40 and 70 by Prime Factorization?

To find the LCM of 40 and 70 using prime factorization, we will find the prime factors, (40 = 2 × 2 × 2 × 5) and (70 = 2 × 5 × 7). LCM of 40 and 70 is the product of prime factors raised to their respective highest exponent among the numbers 40 and 70.
⇒ LCM of 40, 70 = 2³ × 5¹ × 7¹ = 280.

What is the Least Perfect Square Divisible by 40 and 70?

The least number divisible by 40 and 70 = LCM(40, 70)
LCM of 40 and 70 = 2 × 2 × 2 × 5 × 7 [Incomplete pair(s): 2, 5, 7]
⇒ Least perfect square divisible by each 40 and 70 = LCM(40, 70) × 2 × 5 × 7 = 19600 [Square root of 19600 = √19600 = ±140]
Therefore, 19600 is the required number.

If the LCM of 70 and 40 is 280, Find its GCF.

LCM(70, 40) × GCF(70, 40) = 70 × 40
Since the LCM of 70 and 40 = 280
⇒ 280 × GCF(70, 40) = 2800
Therefore, the GCF (greatest common factor) = 2800/280 = 10.