How to find the Least Common Multiple of 30 and 34?
On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 30 and 34.
Follow the steps below, and let's calculate the LCM of 30 and 34.
Method 1 - Prime factorization
Step 1: Create a list of all the prime factors of the numbers 30 and 34:
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 34
The prime factors of 34 are 2 and 17. Prime factorization of 34 in exponential form is:
34 = 21x171
Step 2: Identify the highest power of each prime number from the above boxes:
21, 31, 51, 171
Step 3: Multiply these values together:
21x31x51x171=510
Step 4: The result:
As seen on the calculation above, we have now obtained the LCM of 30 and 34.
The Least Common Multiple of 30 and 34 is 510.
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, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600
Multiples of 34:
34, 68, 102, 136, 170, 204, 238, 272, 306, 340, 374, 408, 442, 476, 510, 544, 578, 612
Therefore,
LCM(30, 34) = 510