Least Common Multiple  of 30 and 40 is 120

How to find the Least Common Multiple of 30 and 40?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 30 and 40.

Follow the steps below, and let's calculate the LCM of 30 and 40.


Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 30 and 40:

Prime factors of 30

The prime factors of 30 are 2, 3 and 5. Prime factorization of 30 in exponential form is:

30 = 21x31x51

Prime factors of 40

The prime factors of 40 are 2, 2, 2 and 5. Prime factorization of 40 in exponential form is:

40 = 23x51


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

23, 31, 51


Step 3: Multiply these values together:

23x31x51=120


Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 30 and 40.

The Least Common Multiple of 30 and 40 is 120.


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 30:

30, 60, 90, 120, 150, 180, 210

Multiples of 40:

40, 80, 120, 160, 200, 240


Therefore,

LCM(30, 40) = 120