Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3706 and 3712 the smallest integer that is 6878336 that is divisible by both numbers.
Least Common Multiple (LCM) of 3706 and 3712 is 6878336.
LCM(3706,3712) = 6878336
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 3706 and 3712. First we will calculate the prime factors of 3706 and 3712.
Prime Factorization of 3706
2 | 3706 |
17 | 1853 |
109 | 109 |
1 |
Prime factors of 3706 are 2, 17,109. Prime factorization of 3706 in exponential form is:
3706 = 21×171×1091
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 3706 and 3712.
LCM(3706,3712) = 27×171×291×1091
LCM(3706,3712) = 6878336
Factors of 3706
List of positive integer factors of 3706 that divides 3706 without a remainder.
1, 2, 17, 34, 109, 218, 1853, 3706
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
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3706 and 3712, than apply into the LCM equation.
GCF(3706,3712) = 2
LCM(3706,3712) = ( 3706 × 3712) / 2
LCM(3706,3712) = 13756672 / 2
LCM(3706,3712) = 6878336
(i) The LCM of 3712 and 3706 is associative
LCM of 3706 and 3712 = LCM of 3712 and 3706
1. What is the LCM of 3706 and 3712?
Answer: LCM of 3706 and 3712 is 6878336.
2. What are the Factors of 3706?
Answer: Factors of 3706 are 1, 2, 17, 34, 109, 218, 1853, 3706. There are 8 integers that are factors of 3706. The greatest factor of 3706 is 3706.
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 3706 and 3712?
Answer:
Least Common Multiple of 3706 and 3712 = 6878336
Step 1: Find the prime factorization of 3706
3706 = 2 x 17 x 109
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 = 6878336 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 17 x 29 x 109
Step 4: Therefore, the least common multiple of 3706 and 3712 is 6878336.