Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1723 and 1724 the smallest integer that is 2970452 that is divisible by both numbers.
Least Common Multiple (LCM) of 1723 and 1724 is 2970452.
LCM(1723,1724) = 2970452
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 1723 and 1724. First we will calculate the prime factors of 1723 and 1724.
Prime Factorization of 1723
1723 | 1723 |
1 |
Prime factors of 1723 are 1723. Prime factorization of 1723 in exponential form is:
1723 = 17231
Prime Factorization of 1724
2 | 1724 |
2 | 862 |
431 | 431 |
1 |
Prime factors of 1724 are 2,431. Prime factorization of 1724 in exponential form is:
1724 = 22×4311
Now multiplying the highest exponent prime factors to calculate the LCM of 1723 and 1724.
LCM(1723,1724) = 22×4311×17231
LCM(1723,1724) = 2970452
Factors of 1723
List of positive integer factors of 1723 that divides 1723 without a remainder.
1, 1723
Factors of 1724
List of positive integer factors of 1724 that divides 1724 without a remainder.
1, 2, 4, 431, 862, 1724
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1723 and 1724, than apply into the LCM equation.
GCF(1723,1724) = 1
LCM(1723,1724) = ( 1723 × 1724) / 1
LCM(1723,1724) = 2970452 / 1
LCM(1723,1724) = 2970452
(i) The LCM of 1724 and 1723 is associative
LCM of 1723 and 1724 = LCM of 1724 and 1723
1. What is the LCM of 1723 and 1724?
Answer: LCM of 1723 and 1724 is 2970452.
2. What are the Factors of 1723?
Answer: Factors of 1723 are 1, 1723. There are 2 integers that are factors of 1723. The greatest factor of 1723 is 1723.
3. What are the Factors of 1724?
Answer: Factors of 1724 are 1, 2, 4, 431, 862, 1724. There are 6 integers that are factors of 1724. The greatest factor of 1724 is 1724.
4. How to Find the LCM of 1723 and 1724?
Answer:
Least Common Multiple of 1723 and 1724 = 2970452
Step 1: Find the prime factorization of 1723
1723 = 1723
Step 2: Find the prime factorization of 1724
1724 = 2 x 2 x 431
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2970452 = 2 x 2 x 431 x 1723
Step 4: Therefore, the least common multiple of 1723 and 1724 is 2970452.