LCM of 60 and 700

LCM of 60 and 700 is the smallest number among all common multiples of 60 and 700. The first few multiples of 60 and 700 are (60, 120, 180, 240, . . . ) and (700, 1400, 2100, 2800, 3500, 4200, 4900, . . . ) respectively. There are 3 commonly used methods to find LCM of 60 and 700 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 60 and 700 is 2100.

Explanation:

The LCM of two non-zero integers, x(60) and y(700), is the smallest positive integer m(2100) that is divisible by both x(60) and y(700) without any remainder.

The methods to find the LCM of 60 and 700 are explained below.

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

LCM of 60 and 700 by Division Method

To calculate the LCM of 60 and 700 by the division method, we will divide the numbers(60, 700) by their prime factors (preferably common). The product of these divisors gives the LCM of 60 and 700.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 60 and 700. Write this prime number(2) on the left of the given numbers(60 and 700), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (60, 700) 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 60 and 700 is the product of all prime numbers on the left, i.e. LCM(60, 700) by division method = 2 × 2 × 3 × 5 × 5 × 7 = 2100.

LCM of 60 and 700 by Prime Factorization

Prime factorization of 60 and 700 is (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ and (2 × 2 × 5 × 5 × 7) = 2² × 5² × 7¹ respectively. LCM of 60 and 700 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5² × 7¹ = 2100.
Hence, the LCM of 60 and 700 by prime factorization is 2100.

LCM of 60 and 700 by Listing Multiples

To calculate the LCM of 60 and 700 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 60 (60, 120, 180, 240, . . . ) and 700 (700, 1400, 2100, 2800, 3500, 4200, 4900, . . . . )
• Step 2: The common multiples from the multiples of 60 and 700 are 2100, 4200, . . .
• Step 3: The smallest common multiple of 60 and 700 is 2100.

∴ The least common multiple of 60 and 700 = 2100.

☛ Also Check:

• LCM of 3 and 21 - 21
• LCM of 24 and 27 - 216
• LCM of 3 and 14 - 42
• LCM of 9 and 33 - 99
• LCM of 3 and 13 - 39
• LCM of 36, 48 and 54 - 432
• LCM of 36 and 81 - 324

FAQs on LCM of 60 and 700

What is the LCM of 60 and 700?

The LCM of 60 and 700 is 2100. To find the LCM (least common multiple) of 60 and 700, we need to find the multiples of 60 and 700 (multiples of 60 = 60, 120, 180, 240 . . . . 2100; multiples of 700 = 700, 1400, 2100, 2800) and choose the smallest multiple that is exactly divisible by 60 and 700, i.e., 2100.

What are the Methods to Find LCM of 60 and 700?

The commonly used methods to find the LCM of 60 and 700 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

Which of the following is the LCM of 60 and 700? 2100, 25, 40, 28

The value of LCM of 60, 700 is the smallest common multiple of 60 and 700. The number satisfying the given condition is 2100.

What is the Relation Between GCF and LCM of 60, 700?

The following equation can be used to express the relation between GCF and LCM of 60 and 700, i.e. GCF × LCM = 60 × 700.

If the LCM of 700 and 60 is 2100, Find its GCF.

LCM(700, 60) × GCF(700, 60) = 700 × 60
Since the LCM of 700 and 60 = 2100
⇒ 2100 × GCF(700, 60) = 42000
Therefore, the GCF (greatest common factor) = 42000/2100 = 20.