Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7707 and 7712 the smallest integer that is 59436384 that is divisible by both numbers.
Least Common Multiple (LCM) of 7707 and 7712 is 59436384.
LCM(7707,7712) = 59436384
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 7707 and 7712. First we will calculate the prime factors of 7707 and 7712.
Prime Factorization of 7707
3 | 7707 |
7 | 2569 |
367 | 367 |
1 |
Prime factors of 7707 are 3, 7,367. Prime factorization of 7707 in exponential form is:
7707 = 31×71×3671
Prime Factorization of 7712
2 | 7712 |
2 | 3856 |
2 | 1928 |
2 | 964 |
2 | 482 |
241 | 241 |
1 |
Prime factors of 7712 are 2,241. Prime factorization of 7712 in exponential form is:
7712 = 25×2411
Now multiplying the highest exponent prime factors to calculate the LCM of 7707 and 7712.
LCM(7707,7712) = 25×31×71×2411×3671
LCM(7707,7712) = 59436384
Factors of 7707
List of positive integer factors of 7707 that divides 7707 without a remainder.
1, 3, 7, 21, 367, 1101, 2569, 7707
Factors of 7712
List of positive integer factors of 7712 that divides 7712 without a remainder.
1, 2, 4, 8, 16, 32, 241, 482, 964, 1928, 3856, 7712
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7707 and 7712, than apply into the LCM equation.
GCF(7707,7712) = 1
LCM(7707,7712) = ( 7707 × 7712) / 1
LCM(7707,7712) = 59436384 / 1
LCM(7707,7712) = 59436384
(i) The LCM of 7712 and 7707 is associative
LCM of 7707 and 7712 = LCM of 7712 and 7707
1. What is the LCM of 7707 and 7712?
Answer: LCM of 7707 and 7712 is 59436384.
2. What are the Factors of 7707?
Answer: Factors of 7707 are 1, 3, 7, 21, 367, 1101, 2569, 7707. There are 8 integers that are factors of 7707. The greatest factor of 7707 is 7707.
3. What are the Factors of 7712?
Answer: Factors of 7712 are 1, 2, 4, 8, 16, 32, 241, 482, 964, 1928, 3856, 7712. There are 12 integers that are factors of 7712. The greatest factor of 7712 is 7712.
4. How to Find the LCM of 7707 and 7712?
Answer:
Least Common Multiple of 7707 and 7712 = 59436384
Step 1: Find the prime factorization of 7707
7707 = 3 x 7 x 367
Step 2: Find the prime factorization of 7712
7712 = 2 x 2 x 2 x 2 x 2 x 241
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 59436384 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 241 x 367
Step 4: Therefore, the least common multiple of 7707 and 7712 is 59436384.