LCM of 60 and 100

LCM of 60 and 100 is the smallest number among all common multiples of 60 and 100. The first few multiples of 60 and 100 are (60, 120, 180, 240, . . . ) and (100, 200, 300, 400, 500, 600, 700, . . . ) respectively. There are 3 commonly used methods to find LCM of 60 and 100 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 60 and 100 is 300.

Explanation:

The LCM of two non-zero integers, x(60) and y(100), is the smallest positive integer m(300) that is divisible by both x(60) and y(100) without any remainder.

Let's look at the different methods for finding the LCM of 60 and 100.

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

LCM of 60 and 100 by Prime Factorization

Prime factorization of 60 and 100 is (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ and (2 × 2 × 5 × 5) = 2² × 5² respectively. LCM of 60 and 100 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5² = 300.
Hence, the LCM of 60 and 100 by prime factorization is 300.

LCM of 60 and 100 by Listing Multiples

To calculate the LCM of 60 and 100 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 100 (100, 200, 300, 400, 500, 600, 700, . . . . )
• Step 2: The common multiples from the multiples of 60 and 100 are 300, 600, . . .
• Step 3: The smallest common multiple of 60 and 100 is 300.

∴ The least common multiple of 60 and 100 = 300.

LCM of 60 and 100 by Division Method

To calculate the LCM of 60 and 100 by the division method, we will divide the numbers(60, 100) by their prime factors (preferably common). The product of these divisors gives the LCM of 60 and 100.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 60 and 100. Write this prime number(2) on the left of the given numbers(60 and 100), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (60, 100) 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 100 is the product of all prime numbers on the left, i.e. LCM(60, 100) by division method = 2 × 2 × 3 × 5 × 5 = 300.

☛ Also Check:

• LCM of 186 and 403 - 2418
• LCM of 4 and 5 - 20
• LCM of 207 and 138 - 414
• LCM of 120 and 90 - 360
• LCM of 8, 9 and 25 - 1800
• LCM of 30 and 42 - 210
• LCM of 16 and 48 - 48

FAQs on LCM of 60 and 100

What is the LCM of 60 and 100?

The LCM of 60 and 100 is 300. To find the LCM (least common multiple) of 60 and 100, we need to find the multiples of 60 and 100 (multiples of 60 = 60, 120, 180, 240 . . . . 300; multiples of 100 = 100, 200, 300, 400) and choose the smallest multiple that is exactly divisible by 60 and 100, i.e., 300.

If the LCM of 100 and 60 is 300, Find its GCF.

LCM(100, 60) × GCF(100, 60) = 100 × 60
Since the LCM of 100 and 60 = 300
⇒ 300 × GCF(100, 60) = 6000
Therefore, the greatest common factor (GCF) = 6000/300 = 20.

How to Find the LCM of 60 and 100 by Prime Factorization?

To find the LCM of 60 and 100 using prime factorization, we will find the prime factors, (60 = 2 × 2 × 3 × 5) and (100 = 2 × 2 × 5 × 5). LCM of 60 and 100 is the product of prime factors raised to their respective highest exponent among the numbers 60 and 100.
⇒ LCM of 60, 100 = 2² × 3¹ × 5² = 300.

Which of the following is the LCM of 60 and 100? 300, 12, 11, 30

The value of LCM of 60, 100 is the smallest common multiple of 60 and 100. The number satisfying the given condition is 300.

What is the Least Perfect Square Divisible by 60 and 100?

The least number divisible by 60 and 100 = LCM(60, 100)
LCM of 60 and 100 = 2 × 2 × 3 × 5 × 5 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 60 and 100 = LCM(60, 100) × 3 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.