Least Common Multiple of 3705 and 3712

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3705 and 3712 the smallest integer that is 13752960 that is divisible by both numbers.

Least Common Multiple (LCM) of 3705 and 3712 is 13752960.

LCM(3705,3712) = 13752960

LCM of 3705 and 3712

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

LCM of:
and

Least Common Multiple of 3705 and 3712

LCM of 3705 and 3712 is 13752960

Least common multiple can be found by multiplying the highest exponent prime factors of 3705 and 3712. First we will calculate the prime factors of 3705 and 3712.

Prime Factorization of 3705


3 3705
5 1235
13 247
19 19
1

Prime factors of 3705 are 3, 5, 13,19. Prime factorization of 3705 in exponential form is:

3705 = 31×51×131×191

Prime Factorization of 3712


2 3712
2 1856
2 928
2 464
2 232
2 116
2 58
29 29
1

Prime factors of 3712 are 2,29. Prime factorization of 3712 in exponential form is:

3712 = 27×291

Now multiplying the highest exponent prime factors to calculate the LCM of 3705 and 3712.

LCM(3705,3712) = 27×31×51×131×191×291
LCM(3705,3712) = 13752960

Factors of 3705

List of positive integer factors of 3705 that divides 3705 without a remainder.

1, 3, 5, 13, 15, 19, 39, 57, 65, 95, 195, 247, 285, 741, 1235, 3705

Factors of 3712

List of positive integer factors of 3712 that divides 3712 without a remainder.

1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 128, 232, 464, 928, 1856, 3712

Least Common Multiple of 3705 and 3712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3705 and 3712, than apply into the LCM equation.

GCF(3705,3712) = 1
LCM(3705,3712) = ( 3705 × 3712) / 1
LCM(3705,3712) = 13752960 / 1
LCM(3705,3712) = 13752960

Properties of LCM 3705 and 3712

(i) The LCM of 3712 and 3705 is associative

LCM of 3705 and 3712 = LCM of 3712 and 3705

Related Least Common Multiples of 3705

Related Least Common Multiples of 3712

Frequently Asked Questions on LCM of 3705 and 3712

1. What is the LCM of 3705 and 3712?

Answer: LCM of 3705 and 3712 is 13752960.

2. What are the Factors of 3705?

Answer: Factors of 3705 are 1, 3, 5, 13, 15, 19, 39, 57, 65, 95, 195, 247, 285, 741, 1235, 3705. There are 16 integers that are factors of 3705. The greatest factor of 3705 is 3705.

3. What are the Factors of 3712?

Answer: Factors of 3712 are 1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 128, 232, 464, 928, 1856, 3712. There are 16 integers that are factors of 3712. The greatest factor of 3712 is 3712.

4. How to Find the LCM of 3705 and 3712?

Answer:

Least Common Multiple of 3705 and 3712 = 13752960

Step 1: Find the prime factorization of 3705

3705 = 3 x 5 x 13 x 19

Step 2: Find the prime factorization of 3712

3712 = 2 x 2 x 2 x 2 x 2 x 2 x 2 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 = 13752960 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 13 x 19 x 29

Step 4: Therefore, the least common multiple of 3705 and 3712 is 13752960.