LCM of 10 and 12

LCM of 10 and 12 is the smallest number among all common multiples of 10 and 12. The first few multiples of 10 and 12 are (10, 20, 30, 40, 50, 60, 70, . . . ) and (12, 24, 36, 48, 60, 72, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 12 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 10 and 12 is 60.

Explanation:

The LCM of two non-zero integers, x(10) and y(12), is the smallest positive integer m(60) that is divisible by both x(10) and y(12) without any remainder.

Let's look at the different methods for finding the LCM of 10 and 12.

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

LCM of 10 and 12 by Prime Factorization

Prime factorization of 10 and 12 is (2 × 5) = 2¹ × 5¹ and (2 × 2 × 3) = 2² × 3¹ respectively. LCM of 10 and 12 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ = 60.
Hence, the LCM of 10 and 12 by prime factorization is 60.

LCM of 10 and 12 by Listing Multiples

To calculate the LCM of 10 and 12 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 10 (10, 20, 30, 40, 50, 60, 70, . . . ) and 12 (12, 24, 36, 48, 60, 72, . . . . )
• Step 2: The common multiples from the multiples of 10 and 12 are 60, 120, . . .
• Step 3: The smallest common multiple of 10 and 12 is 60.

∴ The least common multiple of 10 and 12 = 60.

LCM of 10 and 12 by Division Method

To calculate the LCM of 10 and 12 by the division method, we will divide the numbers(10, 12) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 12.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 12. Write this prime number(2) on the left of the given numbers(10 and 12), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (10, 12) 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 10 and 12 is the product of all prime numbers on the left, i.e. LCM(10, 12) by division method = 2 × 2 × 3 × 5 = 60.

☛ Also Check:

• LCM of 8 and 15 - 120
• LCM of 8 and 14 - 56
• LCM of 8 and 13 - 104
• LCM of 8 and 12 - 24
• LCM of 8 and 11 - 88
• LCM of 8 and 10 - 40
• LCM of 75 and 80 - 1200

FAQs on LCM of 10 and 12

What is the LCM of 10 and 12?

The LCM of 10 and 12 is 60. To find the least common multiple (LCM) of 10 and 12, we need to find the multiples of 10 and 12 (multiples of 10 = 10, 20, 30, 40 . . . . 60; multiples of 12 = 12, 24, 36, 48 . . . . 60) and choose the smallest multiple that is exactly divisible by 10 and 12, i.e., 60.

What is the Relation Between GCF and LCM of 10, 12?

The following equation can be used to express the relation between GCF and LCM of 10 and 12, i.e. GCF × LCM = 10 × 12.

If the LCM of 12 and 10 is 60, Find its GCF.

LCM(12, 10) × GCF(12, 10) = 12 × 10
Since the LCM of 12 and 10 = 60
⇒ 60 × GCF(12, 10) = 120
Therefore, the GCF = 120/60 = 2.

What are the Methods to Find LCM of 10 and 12?

The commonly used methods to find the LCM of 10 and 12 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

Which of the following is the LCM of 10 and 12? 10, 20, 2, 60

The value of LCM of 10, 12 is the smallest common multiple of 10 and 12. The number satisfying the given condition is 60.