Least Common Multiple of 9834 and 9840

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9834 and 9840 the smallest integer that is 16127760 that is divisible by both numbers.

Least Common Multiple (LCM) of 9834 and 9840 is 16127760.

LCM(9834,9840) = 16127760

LCM of 9834 and 9840

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

LCM of:
and

Least Common Multiple of 9834 and 9840

LCM of 9834 and 9840 is 16127760

Least common multiple can be found by multiplying the highest exponent prime factors of 9834 and 9840. First we will calculate the prime factors of 9834 and 9840.

Prime Factorization of 9834


2 9834
3 4917
11 1639
149 149
1

Prime factors of 9834 are 2, 3, 11,149. Prime factorization of 9834 in exponential form is:

9834 = 21×31×111×1491

Prime Factorization of 9840


2 9840
2 4920
2 2460
2 1230
3 615
5 205
41 41
1

Prime factors of 9840 are 2, 3, 5,41. Prime factorization of 9840 in exponential form is:

9840 = 24×31×51×411

Now multiplying the highest exponent prime factors to calculate the LCM of 9834 and 9840.

LCM(9834,9840) = 24×31×51×111×411×1491
LCM(9834,9840) = 16127760

Factors of 9834

List of positive integer factors of 9834 that divides 9834 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 149, 298, 447, 894, 1639, 3278, 4917, 9834

Factors of 9840

List of positive integer factors of 9840 that divides 9840 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 41, 48, 60, 80, 82, 120, 123, 164, 205, 240, 246, 328, 410, 492, 615, 656, 820, 984, 1230, 1640, 1968, 2460, 3280, 4920, 9840

Least Common Multiple of 9834 and 9840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9834 and 9840, than apply into the LCM equation.

GCF(9834,9840) = 6
LCM(9834,9840) = ( 9834 × 9840) / 6
LCM(9834,9840) = 96766560 / 6
LCM(9834,9840) = 16127760

Properties of LCM 9834 and 9840

(i) The LCM of 9840 and 9834 is associative

LCM of 9834 and 9840 = LCM of 9840 and 9834

Related Least Common Multiples of 9834

Related Least Common Multiples of 9840

Frequently Asked Questions on LCM of 9834 and 9840

1. What is the LCM of 9834 and 9840?

Answer: LCM of 9834 and 9840 is 16127760.

2. What are the Factors of 9834?

Answer: Factors of 9834 are 1, 2, 3, 6, 11, 22, 33, 66, 149, 298, 447, 894, 1639, 3278, 4917, 9834. There are 16 integers that are factors of 9834. The greatest factor of 9834 is 9834.

3. What are the Factors of 9840?

Answer: Factors of 9840 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 41, 48, 60, 80, 82, 120, 123, 164, 205, 240, 246, 328, 410, 492, 615, 656, 820, 984, 1230, 1640, 1968, 2460, 3280, 4920, 9840. There are 40 integers that are factors of 9840. The greatest factor of 9840 is 9840.

4. How to Find the LCM of 9834 and 9840?

Answer:

Least Common Multiple of 9834 and 9840 = 16127760

Step 1: Find the prime factorization of 9834

9834 = 2 x 3 x 11 x 149

Step 2: Find the prime factorization of 9840

9840 = 2 x 2 x 2 x 2 x 3 x 5 x 41

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

LCM = 16127760 = 2 x 2 x 2 x 2 x 3 x 5 x 11 x 41 x 149

Step 4: Therefore, the least common multiple of 9834 and 9840 is 16127760.