LCM of 140 and 168

LCM of 140 and 168 is the smallest number among all common multiples of 140 and 168. The first few multiples of 140 and 168 are (140, 280, 420, 560, 700, 840, . . . ) and (168, 336, 504, 672, 840, . . . ) respectively. There are 3 commonly used methods to find LCM of 140 and 168 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 140 and 168 is 840.

Explanation:

The LCM of two non-zero integers, x(140) and y(168), is the smallest positive integer m(840) that is divisible by both x(140) and y(168) without any remainder.

Let's look at the different methods for finding the LCM of 140 and 168.

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

LCM of 140 and 168 by Division Method

To calculate the LCM of 140 and 168 by the division method, we will divide the numbers(140, 168) by their prime factors (preferably common). The product of these divisors gives the LCM of 140 and 168.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 140 and 168. Write this prime number(2) on the left of the given numbers(140 and 168), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (140, 168) 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 140 and 168 is the product of all prime numbers on the left, i.e. LCM(140, 168) by division method = 2 × 2 × 2 × 3 × 5 × 7 = 840.

LCM of 140 and 168 by Listing Multiples

To calculate the LCM of 140 and 168 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 140 (140, 280, 420, 560, 700, 840, . . . ) and 168 (168, 336, 504, 672, 840, . . . . )
• Step 2: The common multiples from the multiples of 140 and 168 are 840, 1680, . . .
• Step 3: The smallest common multiple of 140 and 168 is 840.

∴ The least common multiple of 140 and 168 = 840.

LCM of 140 and 168 by Prime Factorization

Prime factorization of 140 and 168 is (2 × 2 × 5 × 7) = 2² × 5¹ × 7¹ and (2 × 2 × 2 × 3 × 7) = 2³ × 3¹ × 7¹ respectively. LCM of 140 and 168 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 5¹ × 7¹ = 840.
Hence, the LCM of 140 and 168 by prime factorization is 840.

☛ Also Check:

• LCM of 5 and 24 - 120
• LCM of 5 and 20 - 20
• LCM of 5 and 16 - 80
• LCM of 5 and 15 - 15
• LCM of 5 and 14 - 70
• LCM of 5 and 13 - 65
• LCM of 5 and 12 - 60

FAQs on LCM of 140 and 168

What is the LCM of 140 and 168?

The LCM of 140 and 168 is 840. To find the least common multiple of 140 and 168, we need to find the multiples of 140 and 168 (multiples of 140 = 140, 280, 420, 560 . . . . 840; multiples of 168 = 168, 336, 504, 672 . . . . 840) and choose the smallest multiple that is exactly divisible by 140 and 168, i.e., 840.

What are the Methods to Find LCM of 140 and 168?

The commonly used methods to find the LCM of 140 and 168 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

If the LCM of 168 and 140 is 840, Find its GCF.

LCM(168, 140) × GCF(168, 140) = 168 × 140
Since the LCM of 168 and 140 = 840
⇒ 840 × GCF(168, 140) = 23520
Therefore, the greatest common factor = 23520/840 = 28.

How to Find the LCM of 140 and 168 by Prime Factorization?

To find the LCM of 140 and 168 using prime factorization, we will find the prime factors, (140 = 2 × 2 × 5 × 7) and (168 = 2 × 2 × 2 × 3 × 7). LCM of 140 and 168 is the product of prime factors raised to their respective highest exponent among the numbers 140 and 168.
⇒ LCM of 140, 168 = 2³ × 3¹ × 5¹ × 7¹ = 840.

Which of the following is the LCM of 140 and 168? 30, 840, 21, 45

The value of LCM of 140, 168 is the smallest common multiple of 140 and 168. The number satisfying the given condition is 840.