Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1780 and 1784 the smallest integer that is 793880 that is divisible by both numbers.
Least Common Multiple (LCM) of 1780 and 1784 is 793880.
LCM(1780,1784) = 793880
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 1780 and 1784. First we will calculate the prime factors of 1780 and 1784.
Prime Factorization of 1780
2 | 1780 |
2 | 890 |
5 | 445 |
89 | 89 |
1 |
Prime factors of 1780 are 2, 5,89. Prime factorization of 1780 in exponential form is:
1780 = 22×51×891
Prime Factorization of 1784
2 | 1784 |
2 | 892 |
2 | 446 |
223 | 223 |
1 |
Prime factors of 1784 are 2,223. Prime factorization of 1784 in exponential form is:
1784 = 23×2231
Now multiplying the highest exponent prime factors to calculate the LCM of 1780 and 1784.
LCM(1780,1784) = 23×51×891×2231
LCM(1780,1784) = 793880
Factors of 1780
List of positive integer factors of 1780 that divides 1780 without a remainder.
1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890, 1780
Factors of 1784
List of positive integer factors of 1784 that divides 1784 without a remainder.
1, 2, 4, 8, 223, 446, 892, 1784
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1780 and 1784, than apply into the LCM equation.
GCF(1780,1784) = 4
LCM(1780,1784) = ( 1780 × 1784) / 4
LCM(1780,1784) = 3175520 / 4
LCM(1780,1784) = 793880
(i) The LCM of 1784 and 1780 is associative
LCM of 1780 and 1784 = LCM of 1784 and 1780
1. What is the LCM of 1780 and 1784?
Answer: LCM of 1780 and 1784 is 793880.
2. What are the Factors of 1780?
Answer: Factors of 1780 are 1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890, 1780. There are 12 integers that are factors of 1780. The greatest factor of 1780 is 1780.
3. What are the Factors of 1784?
Answer: Factors of 1784 are 1, 2, 4, 8, 223, 446, 892, 1784. There are 8 integers that are factors of 1784. The greatest factor of 1784 is 1784.
4. How to Find the LCM of 1780 and 1784?
Answer:
Least Common Multiple of 1780 and 1784 = 793880
Step 1: Find the prime factorization of 1780
1780 = 2 x 2 x 5 x 89
Step 2: Find the prime factorization of 1784
1784 = 2 x 2 x 2 x 223
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 793880 = 2 x 2 x 2 x 5 x 89 x 223
Step 4: Therefore, the least common multiple of 1780 and 1784 is 793880.