Find the lcm of 10 and 15

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 10 and 15 is 30.

LCM(10,15) = 30

Least Common Multiple of 10 and 15 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10 and 15, than apply into the LCM equation.

GCF(10,15) = 5
LCM(10,15) = ( 10 × 15) / 5
LCM(10,15) = 150 / 5
LCM(10,15) = 30

Least Common Multiple (LCM) of 10 and 15 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 15. First we will calculate the prime factors of 10 and 15.

Prime Factorization of 10

Prime factors of 10 are 2, 5. Prime factorization of 10 in exponential form is:

10 = 21 × 51

Prime Factorization of 15

Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:

15 = 31 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 10 and 15.

LCM(10,15) = 21 × 51 × 31
LCM(10,15) = 30

The LCM of 10 and 15 is 30.

Steps to find LCM

1. Find the prime factorization of 10
   10 = 2 × 5
2. Find the prime factorization of 15
   15 = 3 × 5
3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

   LCM = 2 × 3 × 5

4. LCM = 30

MathStep (Works offline)

Find least common multiple (LCM) of: 20 & 30 30 & 45 50 & 75 2 & 3 70 & 105 20 & 15 10 & 30 30 & 15 10 & 45 50 & 15 10 & 75 70 & 15 10 & 105

LCM of 10 and 15 is the smallest number among all common multiples of 10 and 15. The first few multiples of 10 and 15 are (10, 20, 30, 40, 50, 60, 70, . . . ) and (15, 30, 45, 60, 75, 90, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 15 - by prime factorization, by division method, and by listing multiples.

What is the LCM of 10 and 15?

Answer: LCM of 10 and 15 is 30.

Explanation:

The LCM of two non-zero integers, x(10) and y(15), is the smallest positive integer m(30) that is divisible by both x(10) and y(15) without any remainder.

Methods to Find LCM of 10 and 15

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

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

LCM of 10 and 15 by Division Method

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

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 15. Write this prime number(2) on the left of the given numbers(10 and 15), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (10, 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 and 15 is the product of all prime numbers on the left, i.e. LCM(10, 15) by division method = 2 × 3 × 5 = 30.

LCM of 10 and 15 by Listing Multiples

To calculate the LCM of 10 and 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, 60, 70, . . . ) and 15 (15, 30, 45, 60, 75, 90, . . . . )
• Step 2: The common multiples from the multiples of 10 and 15 are 30, 60, . . .
• Step 3: The smallest common multiple of 10 and 15 is 30.

∴ The least common multiple of 10 and 15 = 30.

LCM of 10 and 15 by Prime Factorization

Prime factorization of 10 and 15 is (2 × 5) = 21 × 51 and (3 × 5) = 31 × 51 respectively. LCM of 10 and 15 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 51 = 30.
Hence, the LCM of 10 and 15 by prime factorization is 30.

☛ Also Check:

• LCM of 72 and 108 - 216
• LCM of 70 and 90 - 630
• LCM of 7 and 9 - 63
• LCM of 7 and 8 - 56
• LCM of 7 and 7 - 7
• LCM of 7 and 56 - 56
• LCM of 7 and 49 - 49

FAQs on LCM of 10 and 15

What is the LCM of 10 and 15?

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

What is the Least Perfect Square Divisible by 10 and 15?

The least number divisible by 10 and 15 = LCM(10, 15)
LCM of 10 and 15 = 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 10 and 15 = LCM(10, 15) × 2 × 3 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

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

The following equation can be used to express the relation between GCF and LCM of 10 and 15, i.e. GCF × LCM = 10 × 15.

If the LCM of 15 and 10 is 30, Find its GCF.

LCM(15, 10) × GCF(15, 10) = 15 × 10
Since the LCM of 15 and 10 = 30
⇒ 30 × GCF(15, 10) = 150
Therefore, the GCF (greatest common factor) = 150/30 = 5.

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

To find the LCM of 10 and 15 using prime factorization, we will find the prime factors, (10 = 2 × 5) and (15 = 3 × 5). LCM of 10 and 15 is the product of prime factors raised to their respective highest exponent among the numbers 10 and 15.
⇒ LCM of 10, 15 = 21 × 31 × 51 = 30.

What is the HCF and LCM of 10 and 15?

How do you find the LCM of 10?

What is the LCM of 15 5 and 10?