Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1731 and 1732 the smallest integer that is 2998092 that is divisible by both numbers.
Least Common Multiple (LCM) of 1731 and 1732 is 2998092.
LCM(1731,1732) = 2998092
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 1731 and 1732. First we will calculate the prime factors of 1731 and 1732.
Prime Factorization of 1731
3 | 1731 |
577 | 577 |
1 |
Prime factors of 1731 are 3,577. Prime factorization of 1731 in exponential form is:
1731 = 31×5771
Prime Factorization of 1732
2 | 1732 |
2 | 866 |
433 | 433 |
1 |
Prime factors of 1732 are 2,433. Prime factorization of 1732 in exponential form is:
1732 = 22×4331
Now multiplying the highest exponent prime factors to calculate the LCM of 1731 and 1732.
LCM(1731,1732) = 22×31×4331×5771
LCM(1731,1732) = 2998092
Factors of 1731
List of positive integer factors of 1731 that divides 1731 without a remainder.
1, 3, 577, 1731
Factors of 1732
List of positive integer factors of 1732 that divides 1732 without a remainder.
1, 2, 4, 433, 866, 1732
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1731 and 1732, than apply into the LCM equation.
GCF(1731,1732) = 1
LCM(1731,1732) = ( 1731 × 1732) / 1
LCM(1731,1732) = 2998092 / 1
LCM(1731,1732) = 2998092
(i) The LCM of 1732 and 1731 is associative
LCM of 1731 and 1732 = LCM of 1732 and 1731
1. What is the LCM of 1731 and 1732?
Answer: LCM of 1731 and 1732 is 2998092.
2. What are the Factors of 1731?
Answer: Factors of 1731 are 1, 3, 577, 1731. There are 4 integers that are factors of 1731. The greatest factor of 1731 is 1731.
3. What are the Factors of 1732?
Answer: Factors of 1732 are 1, 2, 4, 433, 866, 1732. There are 6 integers that are factors of 1732. The greatest factor of 1732 is 1732.
4. How to Find the LCM of 1731 and 1732?
Answer:
Least Common Multiple of 1731 and 1732 = 2998092
Step 1: Find the prime factorization of 1731
1731 = 3 x 577
Step 2: Find the prime factorization of 1732
1732 = 2 x 2 x 433
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2998092 = 2 x 2 x 3 x 433 x 577
Step 4: Therefore, the least common multiple of 1731 and 1732 is 2998092.