LCM of 60 and 66

LCM of 60 and 66 is the smallest number among all common multiples of 60 and 66. The first few multiples of 60 and 66 are (60, 120, 180, 240, 300, . . . ) and (66, 132, 198, 264, . . . ) respectively. There are 3 commonly used methods to find LCM of 60 and 66 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 60 and 66 is 660.

Explanation:

The LCM of two non-zero integers, x(60) and y(66), is the smallest positive integer m(660) that is divisible by both x(60) and y(66) without any remainder.

Let's look at the different methods for finding the LCM of 60 and 66.

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

LCM of 60 and 66 by Division Method

To calculate the LCM of 60 and 66 by the division method, we will divide the numbers(60, 66) by their prime factors (preferably common). The product of these divisors gives the LCM of 60 and 66.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 60 and 66. Write this prime number(2) on the left of the given numbers(60 and 66), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (60, 66) 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 66 is the product of all prime numbers on the left, i.e. LCM(60, 66) by division method = 2 × 2 × 3 × 5 × 11 = 660.

LCM of 60 and 66 by Listing Multiples

To calculate the LCM of 60 and 66 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, 300, . . . ) and 66 (66, 132, 198, 264, . . . . )
• Step 2: The common multiples from the multiples of 60 and 66 are 660, 1320, . . .
• Step 3: The smallest common multiple of 60 and 66 is 660.

∴ The least common multiple of 60 and 66 = 660.

LCM of 60 and 66 by Prime Factorization

Prime factorization of 60 and 66 is (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ and (2 × 3 × 11) = 2¹ × 3¹ × 11¹ respectively. LCM of 60 and 66 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ × 11¹ = 660.
Hence, the LCM of 60 and 66 by prime factorization is 660.

☛ Also Check:

• LCM of 26 and 91 - 182
• LCM of 16, 24 and 40 - 240
• LCM of 42 and 63 - 126
• LCM of 36 and 40 - 360
• LCM of 5, 7 and 10 - 70
• LCM of 5, 8 and 12 - 120
• LCM of 2, 5 and 6 - 30

FAQs on LCM of 60 and 66

What is the LCM of 60 and 66?

The LCM of 60 and 66 is 660. To find the least common multiple of 60 and 66, we need to find the multiples of 60 and 66 (multiples of 60 = 60, 120, 180, 240 . . . . 660; multiples of 66 = 66, 132, 198, 264 . . . . 660) and choose the smallest multiple that is exactly divisible by 60 and 66, i.e., 660.

If the LCM of 66 and 60 is 660, Find its GCF.

LCM(66, 60) × GCF(66, 60) = 66 × 60
Since the LCM of 66 and 60 = 660
⇒ 660 × GCF(66, 60) = 3960
Therefore, the GCF (greatest common factor) = 3960/660 = 6.

What is the Least Perfect Square Divisible by 60 and 66?

The least number divisible by 60 and 66 = LCM(60, 66)
LCM of 60 and 66 = 2 × 2 × 3 × 5 × 11 [Incomplete pair(s): 3, 5, 11]
⇒ Least perfect square divisible by each 60 and 66 = LCM(60, 66) × 3 × 5 × 11 = 108900 [Square root of 108900 = √108900 = ±330]
Therefore, 108900 is the required number.

Which of the following is the LCM of 60 and 66? 5, 21, 42, 660

The value of LCM of 60, 66 is the smallest common multiple of 60 and 66. The number satisfying the given condition is 660.

What are the Methods to Find LCM of 60 and 66?

The commonly used methods to find the LCM of 60 and 66 are:

• Prime Factorization Method
• Listing Multiples
• Division Method