Least Common Multiple of 2814 and 2820

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2814 and 2820 the smallest integer that is 1322580 that is divisible by both numbers.

Least Common Multiple (LCM) of 2814 and 2820 is 1322580.

LCM(2814,2820) = 1322580

LCM of 2814 and 2820

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

LCM of:
and

Least Common Multiple of 2814 and 2820

LCM of 2814 and 2820 is 1322580

Least common multiple can be found by multiplying the highest exponent prime factors of 2814 and 2820. First we will calculate the prime factors of 2814 and 2820.

Prime Factorization of 2814


2 2814
3 1407
7 469
67 67
1

Prime factors of 2814 are 2, 3, 7,67. Prime factorization of 2814 in exponential form is:

2814 = 21×31×71×671

Prime Factorization of 2820


2 2820
2 1410
3 705
5 235
47 47
1

Prime factors of 2820 are 2, 3, 5,47. Prime factorization of 2820 in exponential form is:

2820 = 22×31×51×471

Now multiplying the highest exponent prime factors to calculate the LCM of 2814 and 2820.

LCM(2814,2820) = 22×31×51×71×471×671
LCM(2814,2820) = 1322580

Factors of 2814

List of positive integer factors of 2814 that divides 2814 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 67, 134, 201, 402, 469, 938, 1407, 2814

Factors of 2820

List of positive integer factors of 2820 that divides 2820 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 47, 60, 94, 141, 188, 235, 282, 470, 564, 705, 940, 1410, 2820

Least Common Multiple of 2814 and 2820 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2814 and 2820, than apply into the LCM equation.

GCF(2814,2820) = 6
LCM(2814,2820) = ( 2814 × 2820) / 6
LCM(2814,2820) = 7935480 / 6
LCM(2814,2820) = 1322580

Properties of LCM 2814 and 2820

(i) The LCM of 2820 and 2814 is associative

LCM of 2814 and 2820 = LCM of 2820 and 2814

Related Least Common Multiples of 2814

Related Least Common Multiples of 2820

Frequently Asked Questions on LCM of 2814 and 2820

1. What is the LCM of 2814 and 2820?

Answer: LCM of 2814 and 2820 is 1322580.

2. What are the Factors of 2814?

Answer: Factors of 2814 are 1, 2, 3, 6, 7, 14, 21, 42, 67, 134, 201, 402, 469, 938, 1407, 2814. There are 16 integers that are factors of 2814. The greatest factor of 2814 is 2814.

3. What are the Factors of 2820?

Answer: Factors of 2820 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 47, 60, 94, 141, 188, 235, 282, 470, 564, 705, 940, 1410, 2820. There are 24 integers that are factors of 2820. The greatest factor of 2820 is 2820.

4. How to Find the LCM of 2814 and 2820?

Answer:

Least Common Multiple of 2814 and 2820 = 1322580

Step 1: Find the prime factorization of 2814

2814 = 2 x 3 x 7 x 67

Step 2: Find the prime factorization of 2820

2820 = 2 x 2 x 3 x 5 x 47

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

LCM = 1322580 = 2 x 2 x 3 x 5 x 7 x 47 x 67

Step 4: Therefore, the least common multiple of 2814 and 2820 is 1322580.