Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1736 and 1744 the smallest integer that is 378448 that is divisible by both numbers.
Least Common Multiple (LCM) of 1736 and 1744 is 378448.
LCM(1736,1744) = 378448
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 1736 and 1744. First we will calculate the prime factors of 1736 and 1744.
Prime Factorization of 1736
2 | 1736 |
2 | 868 |
2 | 434 |
7 | 217 |
31 | 31 |
1 |
Prime factors of 1736 are 2, 7,31. Prime factorization of 1736 in exponential form is:
1736 = 23×71×311
Prime Factorization of 1744
2 | 1744 |
2 | 872 |
2 | 436 |
2 | 218 |
109 | 109 |
1 |
Prime factors of 1744 are 2,109. Prime factorization of 1744 in exponential form is:
1744 = 24×1091
Now multiplying the highest exponent prime factors to calculate the LCM of 1736 and 1744.
LCM(1736,1744) = 24×71×311×1091
LCM(1736,1744) = 378448
Factors of 1736
List of positive integer factors of 1736 that divides 1736 without a remainder.
1, 2, 4, 7, 8, 14, 28, 31, 56, 62, 124, 217, 248, 434, 868, 1736
Factors of 1744
List of positive integer factors of 1744 that divides 1744 without a remainder.
1, 2, 4, 8, 16, 109, 218, 436, 872, 1744
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1736 and 1744, than apply into the LCM equation.
GCF(1736,1744) = 8
LCM(1736,1744) = ( 1736 × 1744) / 8
LCM(1736,1744) = 3027584 / 8
LCM(1736,1744) = 378448
(i) The LCM of 1744 and 1736 is associative
LCM of 1736 and 1744 = LCM of 1744 and 1736
1. What is the LCM of 1736 and 1744?
Answer: LCM of 1736 and 1744 is 378448.
2. What are the Factors of 1736?
Answer: Factors of 1736 are 1, 2, 4, 7, 8, 14, 28, 31, 56, 62, 124, 217, 248, 434, 868, 1736. There are 16 integers that are factors of 1736. The greatest factor of 1736 is 1736.
3. What are the Factors of 1744?
Answer: Factors of 1744 are 1, 2, 4, 8, 16, 109, 218, 436, 872, 1744. There are 10 integers that are factors of 1744. The greatest factor of 1744 is 1744.
4. How to Find the LCM of 1736 and 1744?
Answer:
Least Common Multiple of 1736 and 1744 = 378448
Step 1: Find the prime factorization of 1736
1736 = 2 x 2 x 2 x 7 x 31
Step 2: Find the prime factorization of 1744
1744 = 2 x 2 x 2 x 2 x 109
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 378448 = 2 x 2 x 2 x 2 x 7 x 31 x 109
Step 4: Therefore, the least common multiple of 1736 and 1744 is 378448.