LCM of 60 and 68

LCM of 60 and 68 is the smallest number among all common multiples of 60 and 68. The first few multiples of 60 and 68 are (60, 120, 180, 240, 300, 360, . . . ) and (68, 136, 204, 272, . . . ) respectively. There are 3 commonly used methods to find LCM of 60 and 68 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 60 and 68 is 1020.

Explanation:

The LCM of two non-zero integers, x(60) and y(68), is the smallest positive integer m(1020) that is divisible by both x(60) and y(68) without any remainder.

The methods to find the LCM of 60 and 68 are explained below.

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

LCM of 60 and 68 by Prime Factorization

Prime factorization of 60 and 68 is (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ and (2 × 2 × 17) = 2² × 17¹ respectively. LCM of 60 and 68 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ × 17¹ = 1020.
Hence, the LCM of 60 and 68 by prime factorization is 1020.

LCM of 60 and 68 by Listing Multiples

To calculate the LCM of 60 and 68 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, 360, . . . ) and 68 (68, 136, 204, 272, . . . . )
• Step 2: The common multiples from the multiples of 60 and 68 are 1020, 2040, . . .
• Step 3: The smallest common multiple of 60 and 68 is 1020.

∴ The least common multiple of 60 and 68 = 1020.

LCM of 60 and 68 by Division Method

To calculate the LCM of 60 and 68 by the division method, we will divide the numbers(60, 68) by their prime factors (preferably common). The product of these divisors gives the LCM of 60 and 68.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 60 and 68. Write this prime number(2) on the left of the given numbers(60 and 68), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (60, 68) 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 68 is the product of all prime numbers on the left, i.e. LCM(60, 68) by division method = 2 × 2 × 3 × 5 × 17 = 1020.

☛ Also Check:

• LCM of 64 and 72 - 576
• LCM of 2, 4 and 5 - 20
• LCM of 6, 72 and 120 - 360
• LCM of 12 and 30 - 60
• LCM of 8 and 20 - 40
• LCM of 48 and 72 - 144
• LCM of 9 and 36 - 36

FAQs on LCM of 60 and 68

What is the LCM of 60 and 68?

The LCM of 60 and 68 is 1020. To find the least common multiple of 60 and 68, we need to find the multiples of 60 and 68 (multiples of 60 = 60, 120, 180, 240 . . . . 1020; multiples of 68 = 68, 136, 204, 272 . . . . 1020) and choose the smallest multiple that is exactly divisible by 60 and 68, i.e., 1020.

If the LCM of 68 and 60 is 1020, Find its GCF.

LCM(68, 60) × GCF(68, 60) = 68 × 60
Since the LCM of 68 and 60 = 1020
⇒ 1020 × GCF(68, 60) = 4080
Therefore, the greatest common factor (GCF) = 4080/1020 = 4.

What is the Least Perfect Square Divisible by 60 and 68?

The least number divisible by 60 and 68 = LCM(60, 68)
LCM of 60 and 68 = 2 × 2 × 3 × 5 × 17 [Incomplete pair(s): 3, 5, 17]
⇒ Least perfect square divisible by each 60 and 68 = LCM(60, 68) × 3 × 5 × 17 = 260100 [Square root of 260100 = √260100 = ±510]
Therefore, 260100 is the required number.

What are the Methods to Find LCM of 60 and 68?

The commonly used methods to find the LCM of 60 and 68 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

How to Find the LCM of 60 and 68 by Prime Factorization?

To find the LCM of 60 and 68 using prime factorization, we will find the prime factors, (60 = 2 × 2 × 3 × 5) and (68 = 2 × 2 × 17). LCM of 60 and 68 is the product of prime factors raised to their respective highest exponent among the numbers 60 and 68.
⇒ LCM of 60, 68 = 2² × 3¹ × 5¹ × 17¹ = 1020.