Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 426 and 428 the smallest integer that is 91164 that is divisible by both numbers.
Least Common Multiple (LCM) of 426 and 428 is 91164.
LCM(426,428) = 91164
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 426 and 428. First we will calculate the prime factors of 426 and 428.
Prime Factorization of 426
2 | 426 |
3 | 213 |
71 | 71 |
1 |
Prime factors of 426 are 2, 3,71. Prime factorization of 426 in exponential form is:
426 = 21×31×711
Prime Factorization of 428
2 | 428 |
2 | 214 |
107 | 107 |
1 |
Prime factors of 428 are 2,107. Prime factorization of 428 in exponential form is:
428 = 22×1071
Now multiplying the highest exponent prime factors to calculate the LCM of 426 and 428.
LCM(426,428) = 22×31×711×1071
LCM(426,428) = 91164
Factors of 426
List of positive integer factors of 426 that divides 426 without a remainder.
1, 2, 3, 6, 71, 142, 213, 426
Factors of 428
List of positive integer factors of 428 that divides 428 without a remainder.
1, 2, 4, 107, 214, 428
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 426 and 428, than apply into the LCM equation.
GCF(426,428) = 2
LCM(426,428) = ( 426 × 428) / 2
LCM(426,428) = 182328 / 2
LCM(426,428) = 91164
(i) The LCM of 428 and 426 is associative
LCM of 426 and 428 = LCM of 428 and 426
1. What is the LCM of 426 and 428?
Answer: LCM of 426 and 428 is 91164.
2. What are the Factors of 426?
Answer: Factors of 426 are 1, 2, 3, 6, 71, 142, 213, 426. There are 8 integers that are factors of 426. The greatest factor of 426 is 426.
3. What are the Factors of 428?
Answer: Factors of 428 are 1, 2, 4, 107, 214, 428. There are 6 integers that are factors of 428. The greatest factor of 428 is 428.
4. How to Find the LCM of 426 and 428?
Answer:
Least Common Multiple of 426 and 428 = 91164
Step 1: Find the prime factorization of 426
426 = 2 x 3 x 71
Step 2: Find the prime factorization of 428
428 = 2 x 2 x 107
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 91164 = 2 x 2 x 3 x 71 x 107
Step 4: Therefore, the least common multiple of 426 and 428 is 91164.