Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2282 and 2289 the smallest integer that is 746214 that is divisible by both numbers.
Least Common Multiple (LCM) of 2282 and 2289 is 746214.
LCM(2282,2289) = 746214
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 2282 and 2289. First we will calculate the prime factors of 2282 and 2289.
Prime Factorization of 2282
2 | 2282 |
7 | 1141 |
163 | 163 |
1 |
Prime factors of 2282 are 2, 7,163. Prime factorization of 2282 in exponential form is:
2282 = 21×71×1631
Prime Factorization of 2289
3 | 2289 |
7 | 763 |
109 | 109 |
1 |
Prime factors of 2289 are 3, 7,109. Prime factorization of 2289 in exponential form is:
2289 = 31×71×1091
Now multiplying the highest exponent prime factors to calculate the LCM of 2282 and 2289.
LCM(2282,2289) = 21×31×71×1091×1631
LCM(2282,2289) = 746214
Factors of 2282
List of positive integer factors of 2282 that divides 2282 without a remainder.
1, 2, 7, 14, 163, 326, 1141, 2282
Factors of 2289
List of positive integer factors of 2289 that divides 2289 without a remainder.
1, 3, 7, 21, 109, 327, 763, 2289
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2282 and 2289, than apply into the LCM equation.
GCF(2282,2289) = 7
LCM(2282,2289) = ( 2282 × 2289) / 7
LCM(2282,2289) = 5223498 / 7
LCM(2282,2289) = 746214
(i) The LCM of 2289 and 2282 is associative
LCM of 2282 and 2289 = LCM of 2289 and 2282
1. What is the LCM of 2282 and 2289?
Answer: LCM of 2282 and 2289 is 746214.
2. What are the Factors of 2282?
Answer: Factors of 2282 are 1, 2, 7, 14, 163, 326, 1141, 2282. There are 8 integers that are factors of 2282. The greatest factor of 2282 is 2282.
3. What are the Factors of 2289?
Answer: Factors of 2289 are 1, 3, 7, 21, 109, 327, 763, 2289. There are 8 integers that are factors of 2289. The greatest factor of 2289 is 2289.
4. How to Find the LCM of 2282 and 2289?
Answer:
Least Common Multiple of 2282 and 2289 = 746214
Step 1: Find the prime factorization of 2282
2282 = 2 x 7 x 163
Step 2: Find the prime factorization of 2289
2289 = 3 x 7 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 = 746214 = 2 x 3 x 7 x 109 x 163
Step 4: Therefore, the least common multiple of 2282 and 2289 is 746214.