Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1778 and 1784 the smallest integer that is 1585976 that is divisible by both numbers.
Least Common Multiple (LCM) of 1778 and 1784 is 1585976.
LCM(1778,1784) = 1585976
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 1778 and 1784. First we will calculate the prime factors of 1778 and 1784.
Prime Factorization of 1778
2 | 1778 |
7 | 889 |
127 | 127 |
1 |
Prime factors of 1778 are 2, 7,127. Prime factorization of 1778 in exponential form is:
1778 = 21×71×1271
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 1778 and 1784.
LCM(1778,1784) = 23×71×1271×2231
LCM(1778,1784) = 1585976
Factors of 1778
List of positive integer factors of 1778 that divides 1778 without a remainder.
1, 2, 7, 14, 127, 254, 889, 1778
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 1778 and 1784, than apply into the LCM equation.
GCF(1778,1784) = 2
LCM(1778,1784) = ( 1778 × 1784) / 2
LCM(1778,1784) = 3171952 / 2
LCM(1778,1784) = 1585976
(i) The LCM of 1784 and 1778 is associative
LCM of 1778 and 1784 = LCM of 1784 and 1778
1. What is the LCM of 1778 and 1784?
Answer: LCM of 1778 and 1784 is 1585976.
2. What are the Factors of 1778?
Answer: Factors of 1778 are 1, 2, 7, 14, 127, 254, 889, 1778. There are 8 integers that are factors of 1778. The greatest factor of 1778 is 1778.
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 1778 and 1784?
Answer:
Least Common Multiple of 1778 and 1784 = 1585976
Step 1: Find the prime factorization of 1778
1778 = 2 x 7 x 127
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 = 1585976 = 2 x 2 x 2 x 7 x 127 x 223
Step 4: Therefore, the least common multiple of 1778 and 1784 is 1585976.