Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 417 and 422 the smallest integer that is 175974 that is divisible by both numbers.
Least Common Multiple (LCM) of 417 and 422 is 175974.
LCM(417,422) = 175974
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 417 and 422. First we will calculate the prime factors of 417 and 422.
Prime Factorization of 417
3 | 417 |
139 | 139 |
1 |
Prime factors of 417 are 3,139. Prime factorization of 417 in exponential form is:
417 = 31×1391
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 417 and 422.
LCM(417,422) = 21×31×1391×2111
LCM(417,422) = 175974
Factors of 417
List of positive integer factors of 417 that divides 417 without a remainder.
1, 3, 139, 417
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 417 and 422, than apply into the LCM equation.
GCF(417,422) = 1
LCM(417,422) = ( 417 × 422) / 1
LCM(417,422) = 175974 / 1
LCM(417,422) = 175974
(i) The LCM of 422 and 417 is associative
LCM of 417 and 422 = LCM of 422 and 417
1. What is the LCM of 417 and 422?
Answer: LCM of 417 and 422 is 175974.
2. What are the Factors of 417?
Answer: Factors of 417 are 1, 3, 139, 417. There are 4 integers that are factors of 417. The greatest factor of 417 is 417.
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 417 and 422?
Answer:
Least Common Multiple of 417 and 422 = 175974
Step 1: Find the prime factorization of 417
417 = 3 x 139
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 = 175974 = 2 x 3 x 139 x 211
Step 4: Therefore, the least common multiple of 417 and 422 is 175974.