LCM of 28 and 70

LCM of 28 and 70 is the smallest number among all common multiples of 28 and 70. The first few multiples of 28 and 70 are (28, 56, 84, 112, . . . ) and (70, 140, 210, 280, . . . ) respectively. There are 3 commonly used methods to find LCM of 28 and 70 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 28 and 70 is 140.

Explanation:

The LCM of two non-zero integers, x(28) and y(70), is the smallest positive integer m(140) that is divisible by both x(28) and y(70) without any remainder.

The methods to find the LCM of 28 and 70 are explained below.

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

LCM of 28 and 70 by Listing Multiples

To calculate the LCM of 28 and 70 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 28 (28, 56, 84, 112, . . . ) and 70 (70, 140, 210, 280, . . . . )
• Step 2: The common multiples from the multiples of 28 and 70 are 140, 280, . . .
• Step 3: The smallest common multiple of 28 and 70 is 140.

∴ The least common multiple of 28 and 70 = 140.

LCM of 28 and 70 by Division Method

To calculate the LCM of 28 and 70 by the division method, we will divide the numbers(28, 70) by their prime factors (preferably common). The product of these divisors gives the LCM of 28 and 70.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 28 and 70. Write this prime number(2) on the left of the given numbers(28 and 70), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (28, 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 28 and 70 is the product of all prime numbers on the left, i.e. LCM(28, 70) by division method = 2 × 2 × 5 × 7 = 140.

LCM of 28 and 70 by Prime Factorization

Prime factorization of 28 and 70 is (2 × 2 × 7) = 2² × 7¹ and (2 × 5 × 7) = 2¹ × 5¹ × 7¹ respectively. LCM of 28 and 70 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 5¹ × 7¹ = 140.
Hence, the LCM of 28 and 70 by prime factorization is 140.

☛ Also Check:

• LCM of 18 and 54 - 54
• LCM of 18, 24 and 30 - 360
• LCM of 4 and 6 - 12
• LCM of 49 and 63 - 441
• LCM of 2, 3 and 7 - 42
• LCM of 36 and 45 - 180
• LCM of 13 and 91 - 91

FAQs on LCM of 28 and 70

What is the LCM of 28 and 70?

The LCM of 28 and 70 is 140. To find the LCM (least common multiple) of 28 and 70, we need to find the multiples of 28 and 70 (multiples of 28 = 28, 56, 84, 112 . . . . 140; multiples of 70 = 70, 140, 210, 280) and choose the smallest multiple that is exactly divisible by 28 and 70, i.e., 140.

What are the Methods to Find LCM of 28 and 70?

The commonly used methods to find the LCM of 28 and 70 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

If the LCM of 70 and 28 is 140, Find its GCF.

LCM(70, 28) × GCF(70, 28) = 70 × 28
Since the LCM of 70 and 28 = 140
⇒ 140 × GCF(70, 28) = 1960
Therefore, the GCF (greatest common factor) = 1960/140 = 14.

What is the Least Perfect Square Divisible by 28 and 70?

The least number divisible by 28 and 70 = LCM(28, 70)
LCM of 28 and 70 = 2 × 2 × 5 × 7 [Incomplete pair(s): 5, 7]
⇒ Least perfect square divisible by each 28 and 70 = LCM(28, 70) × 5 × 7 = 4900 [Square root of 4900 = √4900 = ±70]
Therefore, 4900 is the required number.

What is the Relation Between GCF and LCM of 28, 70?

The following equation can be used to express the relation between GCF and LCM of 28 and 70, i.e. GCF × LCM = 28 × 70.