Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 407 and 412 the smallest integer that is 167684 that is divisible by both numbers.
Least Common Multiple (LCM) of 407 and 412 is 167684.
LCM(407,412) = 167684
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 407 and 412. First we will calculate the prime factors of 407 and 412.
Prime Factorization of 407
11 | 407 |
37 | 37 |
1 |
Prime factors of 407 are 11,37. Prime factorization of 407 in exponential form is:
407 = 111×371
Prime Factorization of 412
2 | 412 |
2 | 206 |
103 | 103 |
1 |
Prime factors of 412 are 2,103. Prime factorization of 412 in exponential form is:
412 = 22×1031
Now multiplying the highest exponent prime factors to calculate the LCM of 407 and 412.
LCM(407,412) = 22×111×371×1031
LCM(407,412) = 167684
Factors of 407
List of positive integer factors of 407 that divides 407 without a remainder.
1, 11, 37, 407
Factors of 412
List of positive integer factors of 412 that divides 412 without a remainder.
1, 2, 4, 103, 206, 412
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 407 and 412, than apply into the LCM equation.
GCF(407,412) = 1
LCM(407,412) = ( 407 × 412) / 1
LCM(407,412) = 167684 / 1
LCM(407,412) = 167684
(i) The LCM of 412 and 407 is associative
LCM of 407 and 412 = LCM of 412 and 407
1. What is the LCM of 407 and 412?
Answer: LCM of 407 and 412 is 167684.
2. What are the Factors of 407?
Answer: Factors of 407 are 1, 11, 37, 407. There are 4 integers that are factors of 407. The greatest factor of 407 is 407.
3. What are the Factors of 412?
Answer: Factors of 412 are 1, 2, 4, 103, 206, 412. There are 6 integers that are factors of 412. The greatest factor of 412 is 412.
4. How to Find the LCM of 407 and 412?
Answer:
Least Common Multiple of 407 and 412 = 167684
Step 1: Find the prime factorization of 407
407 = 11 x 37
Step 2: Find the prime factorization of 412
412 = 2 x 2 x 103
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 167684 = 2 x 2 x 11 x 37 x 103
Step 4: Therefore, the least common multiple of 407 and 412 is 167684.