Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1423 and 1428 the smallest integer that is 2032044 that is divisible by both numbers.
Least Common Multiple (LCM) of 1423 and 1428 is 2032044.
LCM(1423,1428) = 2032044
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 1423 and 1428. First we will calculate the prime factors of 1423 and 1428.
Prime Factorization of 1423
1423 | 1423 |
1 |
Prime factors of 1423 are 1423. Prime factorization of 1423 in exponential form is:
1423 = 14231
Prime Factorization of 1428
2 | 1428 |
2 | 714 |
3 | 357 |
7 | 119 |
17 | 17 |
1 |
Prime factors of 1428 are 2, 3, 7,17. Prime factorization of 1428 in exponential form is:
1428 = 22×31×71×171
Now multiplying the highest exponent prime factors to calculate the LCM of 1423 and 1428.
LCM(1423,1428) = 22×31×71×171×14231
LCM(1423,1428) = 2032044
Factors of 1423
List of positive integer factors of 1423 that divides 1423 without a remainder.
1, 1423
Factors of 1428
List of positive integer factors of 1428 that divides 1428 without a remainder.
1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, 1428
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1423 and 1428, than apply into the LCM equation.
GCF(1423,1428) = 1
LCM(1423,1428) = ( 1423 × 1428) / 1
LCM(1423,1428) = 2032044 / 1
LCM(1423,1428) = 2032044
(i) The LCM of 1428 and 1423 is associative
LCM of 1423 and 1428 = LCM of 1428 and 1423
1. What is the LCM of 1423 and 1428?
Answer: LCM of 1423 and 1428 is 2032044.
2. What are the Factors of 1423?
Answer: Factors of 1423 are 1, 1423. There are 2 integers that are factors of 1423. The greatest factor of 1423 is 1423.
3. What are the Factors of 1428?
Answer: Factors of 1428 are 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, 1428. There are 24 integers that are factors of 1428. The greatest factor of 1428 is 1428.
4. How to Find the LCM of 1423 and 1428?
Answer:
Least Common Multiple of 1423 and 1428 = 2032044
Step 1: Find the prime factorization of 1423
1423 = 1423
Step 2: Find the prime factorization of 1428
1428 = 2 x 2 x 3 x 7 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2032044 = 2 x 2 x 3 x 7 x 17 x 1423
Step 4: Therefore, the least common multiple of 1423 and 1428 is 2032044.