Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3690 and 3696 the smallest integer that is 2273040 that is divisible by both numbers.
Least Common Multiple (LCM) of 3690 and 3696 is 2273040.
LCM(3690,3696) = 2273040
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 3690 and 3696. First we will calculate the prime factors of 3690 and 3696.
Prime Factorization of 3690
2 | 3690 |
3 | 1845 |
3 | 615 |
5 | 205 |
41 | 41 |
1 |
Prime factors of 3690 are 2, 3, 5,41. Prime factorization of 3690 in exponential form is:
3690 = 21×32×51×411
Prime Factorization of 3696
2 | 3696 |
2 | 1848 |
2 | 924 |
2 | 462 |
3 | 231 |
7 | 77 |
11 | 11 |
1 |
Prime factors of 3696 are 2, 3, 7,11. Prime factorization of 3696 in exponential form is:
3696 = 24×31×71×111
Now multiplying the highest exponent prime factors to calculate the LCM of 3690 and 3696.
LCM(3690,3696) = 24×32×51×71×111×411
LCM(3690,3696) = 2273040
Factors of 3690
List of positive integer factors of 3690 that divides 3690 without a remainder.
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 41, 45, 82, 90, 123, 205, 246, 369, 410, 615, 738, 1230, 1845, 3690
Factors of 3696
List of positive integer factors of 3696 that divides 3696 without a remainder.
1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 33, 42, 44, 48, 56, 66, 77, 84, 88, 112, 132, 154, 168, 176, 231, 264, 308, 336, 462, 528, 616, 924, 1232, 1848, 3696
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3690 and 3696, than apply into the LCM equation.
GCF(3690,3696) = 6
LCM(3690,3696) = ( 3690 × 3696) / 6
LCM(3690,3696) = 13638240 / 6
LCM(3690,3696) = 2273040
(i) The LCM of 3696 and 3690 is associative
LCM of 3690 and 3696 = LCM of 3696 and 3690
1. What is the LCM of 3690 and 3696?
Answer: LCM of 3690 and 3696 is 2273040.
2. What are the Factors of 3690?
Answer: Factors of 3690 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 41, 45, 82, 90, 123, 205, 246, 369, 410, 615, 738, 1230, 1845, 3690. There are 24 integers that are factors of 3690. The greatest factor of 3690 is 3690.
3. What are the Factors of 3696?
Answer: Factors of 3696 are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 33, 42, 44, 48, 56, 66, 77, 84, 88, 112, 132, 154, 168, 176, 231, 264, 308, 336, 462, 528, 616, 924, 1232, 1848, 3696. There are 40 integers that are factors of 3696. The greatest factor of 3696 is 3696.
4. How to Find the LCM of 3690 and 3696?
Answer:
Least Common Multiple of 3690 and 3696 = 2273040
Step 1: Find the prime factorization of 3690
3690 = 2 x 3 x 3 x 5 x 41
Step 2: Find the prime factorization of 3696
3696 = 2 x 2 x 2 x 2 x 3 x 7 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2273040 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 11 x 41
Step 4: Therefore, the least common multiple of 3690 and 3696 is 2273040.