Least Common Multiple of 1407 and 1412

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1407 and 1412 the smallest integer that is 1986684 that is divisible by both numbers.

Least Common Multiple (LCM) of 1407 and 1412 is 1986684.

LCM(1407,1412) = 1986684

LCM of 1407 and 1412

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 1407 and 1412

LCM of 1407 and 1412 is 1986684

Least common multiple can be found by multiplying the highest exponent prime factors of 1407 and 1412. First we will calculate the prime factors of 1407 and 1412.

Prime Factorization of 1407


3 1407
7 469
67 67
1

Prime factors of 1407 are 3, 7,67. Prime factorization of 1407 in exponential form is:

1407 = 31×71×671

Prime Factorization of 1412


2 1412
2 706
353 353
1

Prime factors of 1412 are 2,353. Prime factorization of 1412 in exponential form is:

1412 = 22×3531

Now multiplying the highest exponent prime factors to calculate the LCM of 1407 and 1412.

LCM(1407,1412) = 22×31×71×671×3531
LCM(1407,1412) = 1986684

Factors of 1407

List of positive integer factors of 1407 that divides 1407 without a remainder.

1, 3, 7, 21, 67, 201, 469, 1407

Factors of 1412

List of positive integer factors of 1412 that divides 1412 without a remainder.

1, 2, 4, 353, 706, 1412

Least Common Multiple of 1407 and 1412 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1407 and 1412, than apply into the LCM equation.

GCF(1407,1412) = 1
LCM(1407,1412) = ( 1407 × 1412) / 1
LCM(1407,1412) = 1986684 / 1
LCM(1407,1412) = 1986684

Properties of LCM 1407 and 1412

(i) The LCM of 1412 and 1407 is associative

LCM of 1407 and 1412 = LCM of 1412 and 1407

Related Least Common Multiples of 1407

Related Least Common Multiples of 1412

Frequently Asked Questions on LCM of 1407 and 1412

1. What is the LCM of 1407 and 1412?

Answer: LCM of 1407 and 1412 is 1986684.

2. What are the Factors of 1407?

Answer: Factors of 1407 are 1, 3, 7, 21, 67, 201, 469, 1407. There are 8 integers that are factors of 1407. The greatest factor of 1407 is 1407.

3. What are the Factors of 1412?

Answer: Factors of 1412 are 1, 2, 4, 353, 706, 1412. There are 6 integers that are factors of 1412. The greatest factor of 1412 is 1412.

4. How to Find the LCM of 1407 and 1412?

Answer:

Least Common Multiple of 1407 and 1412 = 1986684

Step 1: Find the prime factorization of 1407

1407 = 3 x 7 x 67

Step 2: Find the prime factorization of 1412

1412 = 2 x 2 x 353

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 1986684 = 2 x 2 x 3 x 7 x 67 x 353

Step 4: Therefore, the least common multiple of 1407 and 1412 is 1986684.