Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1730 and 1737 the smallest integer that is 3005010 that is divisible by both numbers.
Least Common Multiple (LCM) of 1730 and 1737 is 3005010.
LCM(1730,1737) = 3005010
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 1730 and 1737. First we will calculate the prime factors of 1730 and 1737.
Prime Factorization of 1730
2 | 1730 |
5 | 865 |
173 | 173 |
1 |
Prime factors of 1730 are 2, 5,173. Prime factorization of 1730 in exponential form is:
1730 = 21×51×1731
Prime Factorization of 1737
3 | 1737 |
3 | 579 |
193 | 193 |
1 |
Prime factors of 1737 are 3,193. Prime factorization of 1737 in exponential form is:
1737 = 32×1931
Now multiplying the highest exponent prime factors to calculate the LCM of 1730 and 1737.
LCM(1730,1737) = 21×32×51×1731×1931
LCM(1730,1737) = 3005010
Factors of 1730
List of positive integer factors of 1730 that divides 1730 without a remainder.
1, 2, 5, 10, 173, 346, 865, 1730
Factors of 1737
List of positive integer factors of 1737 that divides 1737 without a remainder.
1, 3, 9, 193, 579, 1737
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1730 and 1737, than apply into the LCM equation.
GCF(1730,1737) = 1
LCM(1730,1737) = ( 1730 × 1737) / 1
LCM(1730,1737) = 3005010 / 1
LCM(1730,1737) = 3005010
(i) The LCM of 1737 and 1730 is associative
LCM of 1730 and 1737 = LCM of 1737 and 1730
1. What is the LCM of 1730 and 1737?
Answer: LCM of 1730 and 1737 is 3005010.
2. What are the Factors of 1730?
Answer: Factors of 1730 are 1, 2, 5, 10, 173, 346, 865, 1730. There are 8 integers that are factors of 1730. The greatest factor of 1730 is 1730.
3. What are the Factors of 1737?
Answer: Factors of 1737 are 1, 3, 9, 193, 579, 1737. There are 6 integers that are factors of 1737. The greatest factor of 1737 is 1737.
4. How to Find the LCM of 1730 and 1737?
Answer:
Least Common Multiple of 1730 and 1737 = 3005010
Step 1: Find the prime factorization of 1730
1730 = 2 x 5 x 173
Step 2: Find the prime factorization of 1737
1737 = 3 x 3 x 193
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3005010 = 2 x 3 x 3 x 5 x 173 x 193
Step 4: Therefore, the least common multiple of 1730 and 1737 is 3005010.