What is the least common multiple of 3 and 10

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 3 and 10.

Follow the steps below, and let's calculate the LCM of 3 and 10.

Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 3 and 10:

The prime factors of 3 are 3. Prime factorization of 3 in exponential form is:

3 = 31

The prime factors of 10 are 2 and 5. Prime factorization of 10 in exponential form is:

10 = 21x51

Step 2: Identify the highest power of each prime number from the above boxes:

Step 3: Multiply these values together:

Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 3 and 10.

The Least Common Multiple of 3 and 10 is 30.

Method 2 - List of Multiples

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 3:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39

Multiples of 10:

Therefore,

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 3 and 10 is 30.

LCM(3,10) = 30

Least Common Multiple of 3 and 10 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 10, than apply into the LCM equation.

GCF(3,10) = 1 LCM(3,10) = ( 3 × 10) / 1 LCM(3,10) = 30 / 1

LCM(3,10) = 30

Least Common Multiple (LCM) of 3 and 10 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 10. First we will calculate the prime factors of 3 and 10.

Prime Factorization of 3

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

3 = 31

Prime Factorization of 10

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

10 = 21 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 10.

LCM(3,10) = 31 × 21 × 51
LCM(3,10) = 30

The LCM of 3 and 10 is 30.

Steps to find LCM

1. Find the prime factorization of 3
   3 = 3
2. Find the prime factorization of 10
   10 = 2 × 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: 6 & 20 9 & 30 15 & 50 21 & 70 6 & 10 3 & 20 9 & 10 3 & 30 15 & 10 3 & 50 21 & 10 3 & 70

Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.

LCM(3, 10) = 2×3×5 = 30

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