LCM of 90 and 140

LCM of 90 and 140 is the smallest number among all common multiples of 90 and 140. The first few multiples of 90 and 140 are (90, 180, 270, 360, 450, 540, . . . ) and (140, 280, 420, 560, . . . ) respectively. There are 3 commonly used methods to find LCM of 90 and 140 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 90 and 140 is 1260.

Explanation:

The LCM of two non-zero integers, x(90) and y(140), is the smallest positive integer m(1260) that is divisible by both x(90) and y(140) without any remainder.

Let's look at the different methods for finding the LCM of 90 and 140.

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

LCM of 90 and 140 by Division Method

To calculate the LCM of 90 and 140 by the division method, we will divide the numbers(90, 140) by their prime factors (preferably common). The product of these divisors gives the LCM of 90 and 140.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 90 and 140. Write this prime number(2) on the left of the given numbers(90 and 140), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (90, 140) 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 90 and 140 is the product of all prime numbers on the left, i.e. LCM(90, 140) by division method = 2 × 2 × 3 × 3 × 5 × 7 = 1260.

LCM of 90 and 140 by Listing Multiples

To calculate the LCM of 90 and 140 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 90 (90, 180, 270, 360, 450, 540, . . . ) and 140 (140, 280, 420, 560, . . . . )
• Step 2: The common multiples from the multiples of 90 and 140 are 1260, 2520, . . .
• Step 3: The smallest common multiple of 90 and 140 is 1260.

∴ The least common multiple of 90 and 140 = 1260.

LCM of 90 and 140 by Prime Factorization

Prime factorization of 90 and 140 is (2 × 3 × 3 × 5) = 2¹ × 3² × 5¹ and (2 × 2 × 5 × 7) = 2² × 5¹ × 7¹ respectively. LCM of 90 and 140 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² × 5¹ × 7¹ = 1260.
Hence, the LCM of 90 and 140 by prime factorization is 1260.

☛ Also Check:

• LCM of 54 and 60 - 540
• LCM of 90 and 105 - 630
• LCM of 15, 20 and 30 - 60
• LCM of 12, 16, 24 and 36 - 144
• LCM of 8 and 64 - 64
• LCM of 10, 20 and 30 - 60
• LCM of 7 and 11 - 77

FAQs on LCM of 90 and 140

What is the LCM of 90 and 140?

The LCM of 90 and 140 is 1260. To find the least common multiple (LCM) of 90 and 140, we need to find the multiples of 90 and 140 (multiples of 90 = 90, 180, 270, 360 . . . . 1260; multiples of 140 = 140, 280, 420, 560 . . . . 1260) and choose the smallest multiple that is exactly divisible by 90 and 140, i.e., 1260.

What are the Methods to Find LCM of 90 and 140?

The commonly used methods to find the LCM of 90 and 140 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

If the LCM of 140 and 90 is 1260, Find its GCF.

LCM(140, 90) × GCF(140, 90) = 140 × 90
Since the LCM of 140 and 90 = 1260
⇒ 1260 × GCF(140, 90) = 12600
Therefore, the greatest common factor (GCF) = 12600/1260 = 10.

What is the Relation Between GCF and LCM of 90, 140?

The following equation can be used to express the relation between GCF and LCM of 90 and 140, i.e. GCF × LCM = 90 × 140.

Which of the following is the LCM of 90 and 140? 1260, 5, 18, 50

The value of LCM of 90, 140 is the smallest common multiple of 90 and 140. The number satisfying the given condition is 1260.