How to find the Least Common Multiple of 30 and 38?
On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 30 and 38.
Follow the steps below, and let's calculate the LCM of 30 and 38.
Method 1 - Prime factorization
Step 1: Create a list of all the prime factors of the numbers 30 and 38:
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 38
The prime factors of 38 are 2 and 19. Prime factorization of 38 in exponential form is:
38 = 21x191
Step 2: Identify the highest power of each prime number from the above boxes:
21, 31, 51, 191
Step 3: Multiply these values together:
21x31x51x191=570
Step 4: The result:
As seen on the calculation above, we have now obtained the LCM of 30 and 38.
The Least Common Multiple of 30 and 38 is 570.
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, 630, 660
Multiples of 38:
38, 76, 114, 152, 190, 228, 266, 304, 342, 380, 418, 456, 494, 532, 570, 608, 646, 684
Therefore,
LCM(30, 38) = 570