LCM of 35 and 728

What is the LCM of 35 and 728? - The LCM of 35 and 728 is 3640. Follow the step by step instructions on how to find the least common multiple of 35 and 728.

What is the least common multiple of 35 and 728?

How to find the lcm of 35 and 728?

To find the lcm of 35 and 728, we first need to find the multiples of 35 and 728 and then choose the least common multiple that are dividable by 35 and 728.

Multiples of 35 = 35, 70, 105, 140, 175, 210, 245, 280, 315, 350, 385, 420, 455, 490, 525, 560, 595, 630, 665, 700, 735, 770, 805, 840, 875, 910, 945, 980, 1015, 1050, 1085, 1120, 1155, 1190, 1225, 1260, 1295, 1330, 1365, 1400, 1435, 1470, 1505, 1540, 1575, 1610, 1645, 1680, 1715, 1750, 1785, 1820, 1855, 1890, 1925, 1960, 1995, 2030, 2065, 2100, 2135, 2170, 2205, 2240, 2275, 2310, 2345, 2380, 2415, 2450, 2485, 2520, 2555, 2590, 2625, 2660, 2695, 2730, 2765, 2800, 2835, 2870, 2905, 2940, 2975, 3010, 3045, 3080, 3115, 3150, 3185, 3220, 3255, 3290, 3325, 3360, 3395, 3430, 3465, 3500, 3535, 3570, 3605, 3640
Multiples of 728 = 728, 1456, 2184, 2912, 3640

The least common multiple of 35 and 728 is 3640, because 3640 is the smallest number that is divisible by both 35 and 728.

Another method to find the least common multiple of 35 and 728 is by using the prime factorization method.
To use prime factorization, we first need to find the prime factors of 35 and 728, and then get the LCM by multiplying the prime factors that are rasied to their highest power from the two sets.

Prime factorization of 35 = 5 x 7
Prime factorization of 728 = 2 x 2 x 2 x 7 x 13 = 2³ x 7 x 13
Prime factors to the highest power = 13 x 2³ x 5 x 7 = 3640