Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7230 and 7234 the smallest integer that is 26150910 that is divisible by both numbers.
Least Common Multiple (LCM) of 7230 and 7234 is 26150910.
LCM(7230,7234) = 26150910
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 7230 and 7234. First we will calculate the prime factors of 7230 and 7234.
Prime Factorization of 7230
2 | 7230 |
3 | 3615 |
5 | 1205 |
241 | 241 |
1 |
Prime factors of 7230 are 2, 3, 5,241. Prime factorization of 7230 in exponential form is:
7230 = 21×31×51×2411
Prime Factorization of 7234
2 | 7234 |
3617 | 3617 |
1 |
Prime factors of 7234 are 2,3617. Prime factorization of 7234 in exponential form is:
7234 = 21×36171
Now multiplying the highest exponent prime factors to calculate the LCM of 7230 and 7234.
LCM(7230,7234) = 21×31×51×2411×36171
LCM(7230,7234) = 26150910
Factors of 7230
List of positive integer factors of 7230 that divides 7230 without a remainder.
1, 2, 3, 5, 6, 10, 15, 30, 241, 482, 723, 1205, 1446, 2410, 3615, 7230
Factors of 7234
List of positive integer factors of 7234 that divides 7234 without a remainder.
1, 2, 3617, 7234
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7230 and 7234, than apply into the LCM equation.
GCF(7230,7234) = 2
LCM(7230,7234) = ( 7230 × 7234) / 2
LCM(7230,7234) = 52301820 / 2
LCM(7230,7234) = 26150910
(i) The LCM of 7234 and 7230 is associative
LCM of 7230 and 7234 = LCM of 7234 and 7230
1. What is the LCM of 7230 and 7234?
Answer: LCM of 7230 and 7234 is 26150910.
2. What are the Factors of 7230?
Answer: Factors of 7230 are 1, 2, 3, 5, 6, 10, 15, 30, 241, 482, 723, 1205, 1446, 2410, 3615, 7230. There are 16 integers that are factors of 7230. The greatest factor of 7230 is 7230.
3. What are the Factors of 7234?
Answer: Factors of 7234 are 1, 2, 3617, 7234. There are 4 integers that are factors of 7234. The greatest factor of 7234 is 7234.
4. How to Find the LCM of 7230 and 7234?
Answer:
Least Common Multiple of 7230 and 7234 = 26150910
Step 1: Find the prime factorization of 7230
7230 = 2 x 3 x 5 x 241
Step 2: Find the prime factorization of 7234
7234 = 2 x 3617
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 26150910 = 2 x 3 x 5 x 241 x 3617
Step 4: Therefore, the least common multiple of 7230 and 7234 is 26150910.