Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1734 and 1741 the smallest integer that is 3018894 that is divisible by both numbers.
Least Common Multiple (LCM) of 1734 and 1741 is 3018894.
LCM(1734,1741) = 3018894
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 1734 and 1741. First we will calculate the prime factors of 1734 and 1741.
Prime Factorization of 1734
2 | 1734 |
3 | 867 |
17 | 289 |
17 | 17 |
1 |
Prime factors of 1734 are 2, 3,17. Prime factorization of 1734 in exponential form is:
1734 = 21×31×172
Prime Factorization of 1741
1741 | 1741 |
1 |
Prime factors of 1741 are 1741. Prime factorization of 1741 in exponential form is:
1741 = 17411
Now multiplying the highest exponent prime factors to calculate the LCM of 1734 and 1741.
LCM(1734,1741) = 21×31×172×17411
LCM(1734,1741) = 3018894
Factors of 1734
List of positive integer factors of 1734 that divides 1734 without a remainder.
1, 2, 3, 6, 17, 34, 51, 102, 289, 578, 867, 1734
Factors of 1741
List of positive integer factors of 1741 that divides 1741 without a remainder.
1, 1741
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1734 and 1741, than apply into the LCM equation.
GCF(1734,1741) = 1
LCM(1734,1741) = ( 1734 × 1741) / 1
LCM(1734,1741) = 3018894 / 1
LCM(1734,1741) = 3018894
(i) The LCM of 1741 and 1734 is associative
LCM of 1734 and 1741 = LCM of 1741 and 1734
1. What is the LCM of 1734 and 1741?
Answer: LCM of 1734 and 1741 is 3018894.
2. What are the Factors of 1734?
Answer: Factors of 1734 are 1, 2, 3, 6, 17, 34, 51, 102, 289, 578, 867, 1734. There are 12 integers that are factors of 1734. The greatest factor of 1734 is 1734.
3. What are the Factors of 1741?
Answer: Factors of 1741 are 1, 1741. There are 2 integers that are factors of 1741. The greatest factor of 1741 is 1741.
4. How to Find the LCM of 1734 and 1741?
Answer:
Least Common Multiple of 1734 and 1741 = 3018894
Step 1: Find the prime factorization of 1734
1734 = 2 x 3 x 17 x 17
Step 2: Find the prime factorization of 1741
1741 = 1741
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3018894 = 2 x 3 x 17 x 17 x 1741
Step 4: Therefore, the least common multiple of 1734 and 1741 is 3018894.