Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 420 and 422 the smallest integer that is 88620 that is divisible by both numbers.
Least Common Multiple (LCM) of 420 and 422 is 88620.
LCM(420,422) = 88620
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 420 and 422. First we will calculate the prime factors of 420 and 422.
Prime Factorization of 420
2 | 420 |
2 | 210 |
3 | 105 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 420 are 2, 3, 5,7. Prime factorization of 420 in exponential form is:
420 = 22×31×51×71
Prime Factorization of 422
2 | 422 |
211 | 211 |
1 |
Prime factors of 422 are 2,211. Prime factorization of 422 in exponential form is:
422 = 21×2111
Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 422.
LCM(420,422) = 22×31×51×71×2111
LCM(420,422) = 88620
Factors of 420
List of positive integer factors of 420 that divides 420 without a remainder.
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
Factors of 422
List of positive integer factors of 422 that divides 422 without a remainder.
1, 2, 211, 422
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 420 and 422, than apply into the LCM equation.
GCF(420,422) = 2
LCM(420,422) = ( 420 × 422) / 2
LCM(420,422) = 177240 / 2
LCM(420,422) = 88620
(i) The LCM of 422 and 420 is associative
LCM of 420 and 422 = LCM of 422 and 420
1. What is the LCM of 420 and 422?
Answer: LCM of 420 and 422 is 88620.
2. What are the Factors of 420?
Answer: Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. There are 24 integers that are factors of 420. The greatest factor of 420 is 420.
3. What are the Factors of 422?
Answer: Factors of 422 are 1, 2, 211, 422. There are 4 integers that are factors of 422. The greatest factor of 422 is 422.
4. How to Find the LCM of 420 and 422?
Answer:
Least Common Multiple of 420 and 422 = 88620
Step 1: Find the prime factorization of 420
420 = 2 x 2 x 3 x 5 x 7
Step 2: Find the prime factorization of 422
422 = 2 x 211
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 88620 = 2 x 2 x 3 x 5 x 7 x 211
Step 4: Therefore, the least common multiple of 420 and 422 is 88620.