How to find the Least Common Multiple of 30 and 42?
On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 30 and 42.
Follow the steps below, and let's calculate the LCM of 30 and 42.
Method 1 - Prime factorization
Step 1: Create a list of all the prime factors of the numbers 30 and 42:
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 42
The prime factors of 42 are 2, 3 and 7. Prime factorization of 42 in exponential form is:
42 = 21x31x71
Step 2: Identify the highest power of each prime number from the above boxes:
21, 31, 51, 71
Step 3: Multiply these values together:
21x31x51x71=210
Step 4: The result:
As seen on the calculation above, we have now obtained the LCM of 30 and 42.
The Least Common Multiple of 30 and 42 is 210.
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, 240, 270, 300
Multiples of 42:
42, 84, 126, 168, 210, 252, 294, 336
Therefore,
LCM(30, 42) = 210