Least Common Multiple of 1410 and 1414

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1410 and 1414 the smallest integer that is 996870 that is divisible by both numbers.

Least Common Multiple (LCM) of 1410 and 1414 is 996870.

LCM(1410,1414) = 996870

LCM of 1410 and 1414

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

LCM of:
and

Least Common Multiple of 1410 and 1414

LCM of 1410 and 1414 is 996870

Least common multiple can be found by multiplying the highest exponent prime factors of 1410 and 1414. First we will calculate the prime factors of 1410 and 1414.

Prime Factorization of 1410


2 1410
3 705
5 235
47 47
1

Prime factors of 1410 are 2, 3, 5,47. Prime factorization of 1410 in exponential form is:

1410 = 21×31×51×471

Prime Factorization of 1414


2 1414
7 707
101 101
1

Prime factors of 1414 are 2, 7,101. Prime factorization of 1414 in exponential form is:

1414 = 21×71×1011

Now multiplying the highest exponent prime factors to calculate the LCM of 1410 and 1414.

LCM(1410,1414) = 21×31×51×71×471×1011
LCM(1410,1414) = 996870

Factors of 1410

List of positive integer factors of 1410 that divides 1410 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705, 1410

Factors of 1414

List of positive integer factors of 1414 that divides 1414 without a remainder.

1, 2, 7, 14, 101, 202, 707, 1414

Least Common Multiple of 1410 and 1414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1410 and 1414, than apply into the LCM equation.

GCF(1410,1414) = 2
LCM(1410,1414) = ( 1410 × 1414) / 2
LCM(1410,1414) = 1993740 / 2
LCM(1410,1414) = 996870

Properties of LCM 1410 and 1414

(i) The LCM of 1414 and 1410 is associative

LCM of 1410 and 1414 = LCM of 1414 and 1410

Related Least Common Multiples of 1410

Related Least Common Multiples of 1414

Frequently Asked Questions on LCM of 1410 and 1414

1. What is the LCM of 1410 and 1414?

Answer: LCM of 1410 and 1414 is 996870.

2. What are the Factors of 1410?

Answer: Factors of 1410 are 1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705, 1410. There are 16 integers that are factors of 1410. The greatest factor of 1410 is 1410.

3. What are the Factors of 1414?

Answer: Factors of 1414 are 1, 2, 7, 14, 101, 202, 707, 1414. There are 8 integers that are factors of 1414. The greatest factor of 1414 is 1414.

4. How to Find the LCM of 1410 and 1414?

Answer:

Least Common Multiple of 1410 and 1414 = 996870

Step 1: Find the prime factorization of 1410

1410 = 2 x 3 x 5 x 47

Step 2: Find the prime factorization of 1414

1414 = 2 x 7 x 101

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

LCM = 996870 = 2 x 3 x 5 x 7 x 47 x 101

Step 4: Therefore, the least common multiple of 1410 and 1414 is 996870.