LCM of 60 and 62

LCM of 60 and 62 is the smallest number among all common multiples of 60 and 62. The first few multiples of 60 and 62 are (60, 120, 180, 240, 300, . . . ) and (62, 124, 186, 248, 310, 372, 434, . . . ) respectively. There are 3 commonly used methods to find LCM of 60 and 62 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 60 and 62 is 1860.

Explanation:

The LCM of two non-zero integers, x(60) and y(62), is the smallest positive integer m(1860) that is divisible by both x(60) and y(62) without any remainder.

Let's look at the different methods for finding the LCM of 60 and 62.

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

LCM of 60 and 62 by Listing Multiples

To calculate the LCM of 60 and 62 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 62 (62, 124, 186, 248, 310, 372, 434, . . . . )
• Step 2: The common multiples from the multiples of 60 and 62 are 1860, 3720, . . .
• Step 3: The smallest common multiple of 60 and 62 is 1860.

∴ The least common multiple of 60 and 62 = 1860.

LCM of 60 and 62 by Division Method

To calculate the LCM of 60 and 62 by the division method, we will divide the numbers(60, 62) by their prime factors (preferably common). The product of these divisors gives the LCM of 60 and 62.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 60 and 62. Write this prime number(2) on the left of the given numbers(60 and 62), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (60, 62) 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 62 is the product of all prime numbers on the left, i.e. LCM(60, 62) by division method = 2 × 2 × 3 × 5 × 31 = 1860.

LCM of 60 and 62 by Prime Factorization

Prime factorization of 60 and 62 is (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ and (2 × 31) = 2¹ × 31¹ respectively. LCM of 60 and 62 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ × 31¹ = 1860.
Hence, the LCM of 60 and 62 by prime factorization is 1860.

☛ Also Check:

• LCM of 10 and 18 - 90
• LCM of 6, 10 and 12 - 60
• LCM of 12, 16, 24 and 36 - 144
• LCM of 24 and 90 - 360
• LCM of 2, 3, 4 and 5 - 60
• LCM of 36, 48 and 54 - 432
• LCM of 6, 12 and 15 - 60

FAQs on LCM of 60 and 62

What is the LCM of 60 and 62?

The LCM of 60 and 62 is 1860. To find the LCM of 60 and 62, we need to find the multiples of 60 and 62 (multiples of 60 = 60, 120, 180, 240 . . . . 1860; multiples of 62 = 62, 124, 186, 248 . . . . 1860) and choose the smallest multiple that is exactly divisible by 60 and 62, i.e., 1860.

If the LCM of 62 and 60 is 1860, Find its GCF.

LCM(62, 60) × GCF(62, 60) = 62 × 60
Since the LCM of 62 and 60 = 1860
⇒ 1860 × GCF(62, 60) = 3720
Therefore, the greatest common factor = 3720/1860 = 2.

What is the Relation Between GCF and LCM of 60, 62?

The following equation can be used to express the relation between GCF and LCM of 60 and 62, i.e. GCF × LCM = 60 × 62.

What is the Least Perfect Square Divisible by 60 and 62?

The least number divisible by 60 and 62 = LCM(60, 62)
LCM of 60 and 62 = 2 × 2 × 3 × 5 × 31 [Incomplete pair(s): 3, 5, 31]
⇒ Least perfect square divisible by each 60 and 62 = LCM(60, 62) × 3 × 5 × 31 = 864900 [Square root of 864900 = √864900 = ±930]
Therefore, 864900 is the required number.

What are the Methods to Find LCM of 60 and 62?

The commonly used methods to find the LCM of 60 and 62 are:

• Prime Factorization Method
• Division Method
• Listing Multiples