Least Common Multiple of 321472 and 321480

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 321472 and 321480 by Prime method
• Least Common Multiple of 321472 and 321480 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 321472 and 321480. First we will calculate the prime factors of 321472 and 321480.

Prime Factorization of 321472

Prime factors of 321472 are 2,5023. Prime factorization of 321472 in exponential form is:

321472 = 2⁶×5023¹

Prime Factorization of 321480

Prime factors of 321480 are 2, 3, 5, 19,47. Prime factorization of 321480 in exponential form is:

321480 = 2³×3²×5¹×19¹×47¹

Now multiplying the highest exponent prime factors to calculate the LCM of 321472 and 321480.

LCM(321472,321480) = 2⁶×3²×5¹×19¹×47¹×5023¹
LCM(321472,321480) = 12918352320

Factors of 321472

List of positive integer factors of 321472 that divides 321472 without a remainder.

1, 2, 4, 8, 16, 32, 64, 5023, 10046, 20092, 40184, 80368, 160736, 321472

Factors of 321480

List of positive integer factors of 321480 that divides 321480 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 30, 36, 38, 40, 45, 47, 57, 60, 72, 76, 90, 94, 95, 114, 120, 141, 152, 171, 180, 188, 190, 228, 235, 282, 285, 342, 360, 376, 380, 423, 456, 470, 564, 570, 684, 705, 760, 846, 855, 893, 940, 1128, 1140, 1368, 1410, 1692, 1710, 1786, 1880, 2115, 2280, 2679, 2820, 3384, 3420, 3572, 4230, 4465, 5358, 5640, 6840, 7144, 8037, 8460, 8930, 10716, 13395, 16074, 16920, 17860, 21432, 26790, 32148, 35720, 40185, 53580, 64296, 80370, 107160, 160740, 321480

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 321472 and 321480, than apply into the LCM equation.

GCF(321472,321480) = 8
LCM(321472,321480) = ( 321472 × 321480) / 8
LCM(321472,321480) = 103346818560 / 8
LCM(321472,321480) = 12918352320

(i) The LCM of 321480 and 321472 is associative

LCM of 321472 and 321480 = LCM of 321480 and 321472

1. What is the LCM of 321472 and 321480?

Answer: LCM of 321472 and 321480 is 12918352320.

2. What are the Factors of 321472?

Answer: Factors of 321472 are 1, 2, 4, 8, 16, 32, 64, 5023, 10046, 20092, 40184, 80368, 160736, 321472. There are 14 integers that are factors of 321472. The greatest factor of 321472 is 321472.

3. What are the Factors of 321480?

Answer: Factors of 321480 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 30, 36, 38, 40, 45, 47, 57, 60, 72, 76, 90, 94, 95, 114, 120, 141, 152, 171, 180, 188, 190, 228, 235, 282, 285, 342, 360, 376, 380, 423, 456, 470, 564, 570, 684, 705, 760, 846, 855, 893, 940, 1128, 1140, 1368, 1410, 1692, 1710, 1786, 1880, 2115, 2280, 2679, 2820, 3384, 3420, 3572, 4230, 4465, 5358, 5640, 6840, 7144, 8037, 8460, 8930, 10716, 13395, 16074, 16920, 17860, 21432, 26790, 32148, 35720, 40185, 53580, 64296, 80370, 107160, 160740, 321480. There are 96 integers that are factors of 321480. The greatest factor of 321480 is 321480.

4. How to Find the LCM of 321472 and 321480?

Answer:

Least Common Multiple of 321472 and 321480 = 12918352320

Step 1: Find the prime factorization of 321472

321472 = 2 x 2 x 2 x 2 x 2 x 2 x 5023

Step 2: Find the prime factorization of 321480

321480 = 2 x 2 x 2 x 3 x 3 x 5 x 19 x 47

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 12918352320 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 19 x 47 x 5023

Step 4: Therefore, the least common multiple of 321472 and 321480 is 12918352320.