LCM of 208 and 138

What is the LCM of 208 and 138? - The LCM of 208 and 138 is 14352. Follow the step by step instructions on how to find the least common multiple of 208 and 138.

What is the least common multiple of 208 and 138?

How to find the lcm of 208 and 138?

To find the lcm of 208 and 138, we first need to find the multiples of 208 and 138 and then choose the least common multiple that are dividable by 208 and 138.

Multiples of 208 = 208, 416, 624, 832, 1040, 1248, 1456, 1664, 1872, 2080, 2288, 2496, 2704, 2912, 3120, 3328, 3536, 3744, 3952, 4160, 4368, 4576, 4784, 4992, 5200, 5408, 5616, 5824, 6032, 6240, 6448, 6656, 6864, 7072, 7280, 7488, 7696, 7904, 8112, 8320, 8528, 8736, 8944, 9152, 9360, 9568, 9776, 9984, 10192, 10400, 10608, 10816, 11024, 11232, 11440, 11648, 11856, 12064, 12272, 12480, 12688, 12896, 13104, 13312, 13520, 13728, 13936, 14144, 14352
Multiples of 138 = 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380, 1518, 1656, 1794, 1932, 2070, 2208, 2346, 2484, 2622, 2760, 2898, 3036, 3174, 3312, 3450, 3588, 3726, 3864, 4002, 4140, 4278, 4416, 4554, 4692, 4830, 4968, 5106, 5244, 5382, 5520, 5658, 5796, 5934, 6072, 6210, 6348, 6486, 6624, 6762, 6900, 7038, 7176, 7314, 7452, 7590, 7728, 7866, 8004, 8142, 8280, 8418, 8556, 8694, 8832, 8970, 9108, 9246, 9384, 9522, 9660, 9798, 9936, 10074, 10212, 10350, 10488, 10626, 10764, 10902, 11040, 11178, 11316, 11454, 11592, 11730, 11868, 12006, 12144, 12282, 12420, 12558, 12696, 12834, 12972, 13110, 13248, 13386, 13524, 13662, 13800, 13938, 14076, 14214, 14352

The least common multiple of 208 and 138 is 14352, because 14352 is the smallest number that is divisible by both 208 and 138.

Another method to find the least common multiple of 208 and 138 is by using the prime factorization method.
To use prime factorization, we first need to find the prime factors of 208 and 138, and then get the LCM by multiplying the prime factors that are rasied to their highest power from the two sets.

Prime factorization of 208 = 2 x 2 x 2 x 2 x 13 = 2⁴ x 13
Prime factorization of 138 = 2 x 3 x 23
Prime factors to the highest power = 13 x 2⁴ x 23 x 3 = 14352