Least Common Multiple of 1407 and 1415

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 1415 the smallest integer that is 1990905 that is divisible by both numbers.

Least Common Multiple (LCM) of 1407 and 1415 is 1990905.

LCM(1407,1415) = 1990905

LCM of 1407 and 1415

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

LCM of:
and

Least Common Multiple of 1407 and 1415

LCM of 1407 and 1415 is 1990905

Least common multiple can be found by multiplying the highest exponent prime factors of 1407 and 1415. First we will calculate the prime factors of 1407 and 1415.

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 1415


5 1415
283 283
1

Prime factors of 1415 are 5,283. Prime factorization of 1415 in exponential form is:

1415 = 51×2831

Now multiplying the highest exponent prime factors to calculate the LCM of 1407 and 1415.

LCM(1407,1415) = 31×51×71×671×2831
LCM(1407,1415) = 1990905

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 1415

List of positive integer factors of 1415 that divides 1415 without a remainder.

1, 5, 283, 1415

Least Common Multiple of 1407 and 1415 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 1415, than apply into the LCM equation.

GCF(1407,1415) = 1
LCM(1407,1415) = ( 1407 × 1415) / 1
LCM(1407,1415) = 1990905 / 1
LCM(1407,1415) = 1990905

Properties of LCM 1407 and 1415

(i) The LCM of 1415 and 1407 is associative

LCM of 1407 and 1415 = LCM of 1415 and 1407

Related Least Common Multiples of 1407

Related Least Common Multiples of 1415

Frequently Asked Questions on LCM of 1407 and 1415

1. What is the LCM of 1407 and 1415?

Answer: LCM of 1407 and 1415 is 1990905.

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 1415?

Answer: Factors of 1415 are 1, 5, 283, 1415. There are 4 integers that are factors of 1415. The greatest factor of 1415 is 1415.

4. How to Find the LCM of 1407 and 1415?

Answer:

Least Common Multiple of 1407 and 1415 = 1990905

Step 1: Find the prime factorization of 1407

1407 = 3 x 7 x 67

Step 2: Find the prime factorization of 1415

1415 = 5 x 283

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

LCM = 1990905 = 3 x 5 x 7 x 67 x 283

Step 4: Therefore, the least common multiple of 1407 and 1415 is 1990905.