Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 721 and 723 the smallest integer that is 521283 that is divisible by both numbers.
Least Common Multiple (LCM) of 721 and 723 is 521283.
LCM(721,723) = 521283
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 721 and 723. First we will calculate the prime factors of 721 and 723.
Prime Factorization of 721
7 | 721 |
103 | 103 |
1 |
Prime factors of 721 are 7,103. Prime factorization of 721 in exponential form is:
721 = 71×1031
Prime Factorization of 723
3 | 723 |
241 | 241 |
1 |
Prime factors of 723 are 3,241. Prime factorization of 723 in exponential form is:
723 = 31×2411
Now multiplying the highest exponent prime factors to calculate the LCM of 721 and 723.
LCM(721,723) = 31×71×1031×2411
LCM(721,723) = 521283
Factors of 721
List of positive integer factors of 721 that divides 721 without a remainder.
1, 7, 103, 721
Factors of 723
List of positive integer factors of 723 that divides 723 without a remainder.
1, 3, 241, 723
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 721 and 723, than apply into the LCM equation.
GCF(721,723) = 1
LCM(721,723) = ( 721 × 723) / 1
LCM(721,723) = 521283 / 1
LCM(721,723) = 521283
(i) The LCM of 723 and 721 is associative
LCM of 721 and 723 = LCM of 723 and 721
1. What is the LCM of 721 and 723?
Answer: LCM of 721 and 723 is 521283.
2. What are the Factors of 721?
Answer: Factors of 721 are 1, 7, 103, 721. There are 4 integers that are factors of 721. The greatest factor of 721 is 721.
3. What are the Factors of 723?
Answer: Factors of 723 are 1, 3, 241, 723. There are 4 integers that are factors of 723. The greatest factor of 723 is 723.
4. How to Find the LCM of 721 and 723?
Answer:
Least Common Multiple of 721 and 723 = 521283
Step 1: Find the prime factorization of 721
721 = 7 x 103
Step 2: Find the prime factorization of 723
723 = 3 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 = 521283 = 3 x 7 x 103 x 241
Step 4: Therefore, the least common multiple of 721 and 723 is 521283.