Least Common Multiple of 7824 and 7830

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7824 and 7830 the smallest integer that is 10210320 that is divisible by both numbers.

Least Common Multiple (LCM) of 7824 and 7830 is 10210320.

LCM(7824,7830) = 10210320

LCM of 7824 and 7830

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

LCM of:
and

Least Common Multiple of 7824 and 7830

LCM of 7824 and 7830 is 10210320

Least common multiple can be found by multiplying the highest exponent prime factors of 7824 and 7830. First we will calculate the prime factors of 7824 and 7830.

Prime Factorization of 7824


2 7824
2 3912
2 1956
2 978
3 489
163 163
1

Prime factors of 7824 are 2, 3,163. Prime factorization of 7824 in exponential form is:

7824 = 24×31×1631

Prime Factorization of 7830


2 7830
3 3915
3 1305
3 435
5 145
29 29
1

Prime factors of 7830 are 2, 3, 5,29. Prime factorization of 7830 in exponential form is:

7830 = 21×33×51×291

Now multiplying the highest exponent prime factors to calculate the LCM of 7824 and 7830.

LCM(7824,7830) = 24×33×51×291×1631
LCM(7824,7830) = 10210320

Factors of 7824

List of positive integer factors of 7824 that divides 7824 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 163, 326, 489, 652, 978, 1304, 1956, 2608, 3912, 7824

Factors of 7830

List of positive integer factors of 7830 that divides 7830 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 29, 30, 45, 54, 58, 87, 90, 135, 145, 174, 261, 270, 290, 435, 522, 783, 870, 1305, 1566, 2610, 3915, 7830

Least Common Multiple of 7824 and 7830 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7824 and 7830, than apply into the LCM equation.

GCF(7824,7830) = 6
LCM(7824,7830) = ( 7824 × 7830) / 6
LCM(7824,7830) = 61261920 / 6
LCM(7824,7830) = 10210320

Properties of LCM 7824 and 7830

(i) The LCM of 7830 and 7824 is associative

LCM of 7824 and 7830 = LCM of 7830 and 7824

Related Least Common Multiples of 7824

Related Least Common Multiples of 7830

Frequently Asked Questions on LCM of 7824 and 7830

1. What is the LCM of 7824 and 7830?

Answer: LCM of 7824 and 7830 is 10210320.

2. What are the Factors of 7824?

Answer: Factors of 7824 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 163, 326, 489, 652, 978, 1304, 1956, 2608, 3912, 7824. There are 20 integers that are factors of 7824. The greatest factor of 7824 is 7824.

3. What are the Factors of 7830?

Answer: Factors of 7830 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 29, 30, 45, 54, 58, 87, 90, 135, 145, 174, 261, 270, 290, 435, 522, 783, 870, 1305, 1566, 2610, 3915, 7830. There are 32 integers that are factors of 7830. The greatest factor of 7830 is 7830.

4. How to Find the LCM of 7824 and 7830?

Answer:

Least Common Multiple of 7824 and 7830 = 10210320

Step 1: Find the prime factorization of 7824

7824 = 2 x 2 x 2 x 2 x 3 x 163

Step 2: Find the prime factorization of 7830

7830 = 2 x 3 x 3 x 3 x 5 x 29

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

LCM = 10210320 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 29 x 163

Step 4: Therefore, the least common multiple of 7824 and 7830 is 10210320.