Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7920 and 7923 the smallest integer that is 20916720 that is divisible by both numbers.
Least Common Multiple (LCM) of 7920 and 7923 is 20916720.
LCM(7920,7923) = 20916720
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 7920 and 7923. First we will calculate the prime factors of 7920 and 7923.
Prime Factorization of 7920
2 | 7920 |
2 | 3960 |
2 | 1980 |
2 | 990 |
3 | 495 |
3 | 165 |
5 | 55 |
11 | 11 |
1 |
Prime factors of 7920 are 2, 3, 5,11. Prime factorization of 7920 in exponential form is:
7920 = 24×32×51×111
Prime Factorization of 7923
3 | 7923 |
19 | 2641 |
139 | 139 |
1 |
Prime factors of 7923 are 3, 19,139. Prime factorization of 7923 in exponential form is:
7923 = 31×191×1391
Now multiplying the highest exponent prime factors to calculate the LCM of 7920 and 7923.
LCM(7920,7923) = 24×32×51×111×191×1391
LCM(7920,7923) = 20916720
Factors of 7920
List of positive integer factors of 7920 that divides 7920 without a remainder.
1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 48, 55, 60, 66, 72, 80, 88, 90, 99, 110, 120, 132, 144, 165, 176, 180, 198, 220, 240, 264, 330, 360, 396, 440, 495, 528, 660, 720, 792, 880, 990, 1320, 1584, 1980, 2640, 3960, 7920
Factors of 7923
List of positive integer factors of 7923 that divides 7923 without a remainder.
1, 3, 19, 57, 139, 417, 2641, 7923
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7920 and 7923, than apply into the LCM equation.
GCF(7920,7923) = 3
LCM(7920,7923) = ( 7920 × 7923) / 3
LCM(7920,7923) = 62750160 / 3
LCM(7920,7923) = 20916720
(i) The LCM of 7923 and 7920 is associative
LCM of 7920 and 7923 = LCM of 7923 and 7920
1. What is the LCM of 7920 and 7923?
Answer: LCM of 7920 and 7923 is 20916720.
2. What are the Factors of 7920?
Answer: Factors of 7920 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 48, 55, 60, 66, 72, 80, 88, 90, 99, 110, 120, 132, 144, 165, 176, 180, 198, 220, 240, 264, 330, 360, 396, 440, 495, 528, 660, 720, 792, 880, 990, 1320, 1584, 1980, 2640, 3960, 7920. There are 60 integers that are factors of 7920. The greatest factor of 7920 is 7920.
3. What are the Factors of 7923?
Answer: Factors of 7923 are 1, 3, 19, 57, 139, 417, 2641, 7923. There are 8 integers that are factors of 7923. The greatest factor of 7923 is 7923.
4. How to Find the LCM of 7920 and 7923?
Answer:
Least Common Multiple of 7920 and 7923 = 20916720
Step 1: Find the prime factorization of 7920
7920 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11
Step 2: Find the prime factorization of 7923
7923 = 3 x 19 x 139
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 20916720 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11 x 19 x 139
Step 4: Therefore, the least common multiple of 7920 and 7923 is 20916720.