LCM of 10, 12, and 15

LCM of 10, 12, and 15 is the smallest number among all common multiples of 10, 12, and 15. The first few multiples of 10, 12, and 15 are (10, 20, 30, 40, 50 . . .), (12, 24, 36, 48, 60 . . .), and (15, 30, 45, 60, 75 . . .) respectively. There are 3 commonly used methods to find LCM of 10, 12, 15 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 10, 12, and 15 is 60.

Explanation:

The LCM of three non-zero integers, a(10), b(12), and c(15), is the smallest positive integer m(60) that is divisible by a(10), b(12), and c(15) without any remainder.

The methods to find the LCM of 10, 12, and 15 are explained below.

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

LCM of 10, 12, and 15 by Prime Factorization

Prime factorization of 10, 12, and 15 is (2 × 5) = 2¹ × 5¹, (2 × 2 × 3) = 2² × 3¹, and (3 × 5) = 3¹ × 5¹ respectively. LCM of 10, 12, and 15 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ = 60.
Hence, the LCM of 10, 12, and 15 by prime factorization is 60.

LCM of 10, 12, and 15 by Division Method

To calculate the LCM of 10, 12, and 15 by the division method, we will divide the numbers(10, 12, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 10, 12, and 15.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10, 12, and 15. Write this prime number(2) on the left of the given numbers(10, 12, and 15), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (10, 12, 15) 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, 12, and 15 is the product of all prime numbers on the left, i.e. LCM(10, 12, 15) by division method = 2 × 2 × 3 × 5 = 60.

LCM of 10, 12, and 15 by Listing Multiples

To calculate the LCM of 10, 12, 15 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 . . .), 12 (12, 24, 36, 48, 60 . . .), and 15 (15, 30, 45, 60, 75 . . .).
• Step 2: The common multiples from the multiples of 10, 12, and 15 are 60, 120, . . .
• Step 3: The smallest common multiple of 10, 12, and 15 is 60.

∴ The least common multiple of 10, 12, and 15 = 60.

☛ Also Check:

• LCM of 36 and 40 - 360
• LCM of 5 and 13 - 65
• LCM of 18 and 32 - 288
• LCM of 6 and 30 - 30
• LCM of 2 and 9 - 18
• LCM of 24, 36, 44 and 62 - 24552
• LCM of 11 and 13 - 143

FAQs on LCM of 10, 12, and 15

What is the LCM of 10, 12, and 15?

The LCM of 10, 12, and 15 is 60. To find the LCM (least common multiple) of 10, 12, and 15, we need to find the multiples of 10, 12, and 15 (multiples of 10 = 10, 20, 30, 40, 60 . . . .; multiples of 12 = 12, 24, 36, 48 . . . . 60 . . . . ; multiples of 15 = 15, 30, 45, 60 . . . .) and choose the smallest multiple that is exactly divisible by 10, 12, and 15, i.e., 60.

Which of the following is the LCM of 10, 12, and 15? 18, 60, 27, 11

The value of LCM of 10, 12, 15 is the smallest common multiple of 10, 12, and 15. The number satisfying the given condition is 60.

What is the Relation Between GCF and LCM of 10, 12, 15?

The following equation can be used to express the relation between GCF and LCM of 10, 12, 15, i.e. LCM(10, 12, 15) = [(10 × 12 × 15) × GCF(10, 12, 15)]/[GCF(10, 12) × GCF(12, 15) × GCF(10, 15)].

How to Find the LCM of 10, 12, and 15 by Prime Factorization?

To find the LCM of 10, 12, and 15 using prime factorization, we will find the prime factors, (10 = 2¹ × 5¹), (12 = 2² × 3¹), and (15 = 3¹ × 5¹). LCM of 10, 12, and 15 is the product of prime factors raised to their respective highest exponent among the numbers 10, 12, and 15.
⇒ LCM of 10, 12, 15 = 2² × 3¹ × 5¹ = 60.