How to find the Least Common Multiple of 54 and 65?
On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 54 and 65.
Follow the steps below, and let's calculate the LCM of 54 and 65.
Method 1 - Prime factorization
Step 1: Create a list of all the prime factors of the numbers 54 and 65:
Prime factors of 54
The prime factors of 54 are 2, 3, 3 and 3. Prime factorization of 54 in exponential form is:
54 = 21x33
Prime factors of 65
The prime factors of 65 are 5 and 13. Prime factorization of 65 in exponential form is:
65 = 51x131
Step 2: Identify the highest power of each prime number from the above boxes:
21, 33, 51, 131
Step 3: Multiply these values together:
21x33x51x131=3510
Step 4: The result:
As seen on the calculation above, we have now obtained the LCM of 54 and 65.
The Least Common Multiple of 54 and 65 is 3510.
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 54:
54, 108, 162, 216, 270, 324, 378, 432, 486, 540, 594, 648, 702, 756, 810, 864, 918, 972, 1026, 1080, 1134, 1188, 1242, 1296, 1350, 1404, 1458, 1512, 1566, 1620, 1674, 1728, 1782, 1836, 1890, 1944, 1998, 2052, 2106, 2160, 2214, 2268, 2322, 2376, 2430, 2484, 2538, 2592, 2646, 2700, 2754, 2808, 2862, 2916, 2970, 3024, 3078, 3132, 3186, 3240, 3294, 3348, 3402, 3456, 3510, 3564, 3618, 3672
Multiples of 65:
65, 130, 195, 260, 325, 390, 455, 520, 585, 650, 715, 780, 845, 910, 975, 1040, 1105, 1170, 1235, 1300, 1365, 1430, 1495, 1560, 1625, 1690, 1755, 1820, 1885, 1950, 2015, 2080, 2145, 2210, 2275, 2340, 2405, 2470, 2535, 2600, 2665, 2730, 2795, 2860, 2925, 2990, 3055, 3120, 3185, 3250, 3315, 3380, 3445, 3510, 3575, 3640, 3705
Therefore,
LCM(54, 65) = 3510