Least Common Multiple of 294 and 300
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 294 and 300 the smallest integer that is 14700 that is divisible by both numbers.
Least Common Multiple (LCM) of 294 and 300 is 14700.
LCM(294,300) = 14700
LCM of 294 and 300
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 294 and 300 by Prime method
- Least Common Multiple of 294 and 300 with GCF Formula
LCM of 294 and 300 is 14700
Least common multiple can be found by multiplying the highest exponent prime factors of 294 and 300. First we will calculate the prime factors of 294 and 300.
Prime Factorization of 294
| 2 | 294 |
| 3 | 147 |
| 7 | 49 |
| 7 | 7 |
| 1 |
Prime factors of 294 are 2, 3,7. Prime factorization of 294 in exponential form is:
294 = 21×31×72
Prime Factorization of 300
| 2 | 300 |
| 2 | 150 |
| 3 | 75 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 300 are 2, 3,5. Prime factorization of 300 in exponential form is:
300 = 22×31×52
Now multiplying the highest exponent prime factors to calculate the LCM of 294 and 300.
LCM(294,300) = 22×31×52×72
LCM(294,300) = 14700
Factors of 294
List of positive integer factors of 294 that divides 294 without a remainder.
1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
Factors of 300
List of positive integer factors of 300 that divides 300 without a remainder.
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Least Common Multiple of 294 and 300 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 294 and 300, than apply into the LCM equation.
GCF(294,300) = 6
LCM(294,300) = ( 294 × 300) / 6
LCM(294,300) = 88200 / 6
LCM(294,300) = 14700
Properties of LCM 294 and 300
(i) The LCM of 300 and 294 is associative
LCM of 294 and 300 = LCM of 300 and 294
Related Least Common Multiples of 294
Related Least Common Multiples of 300
Frequently Asked Questions on LCM of 294 and 300
1. What is the LCM of 294 and 300?
Answer: LCM of 294 and 300 is 14700.
2. What are the Factors of 294?
Answer: Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294. There are 12 integers that are factors of 294. The greatest factor of 294 is 294.
3. What are the Factors of 300?
Answer: Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300. There are 18 integers that are factors of 300. The greatest factor of 300 is 300.
4. How to Find the LCM of 294 and 300?
Answer:
Least Common Multiple of 294 and 300 = 14700
Step 1: Find the prime factorization of 294
294 = 2 x 3 x 7 x 7
Step 2: Find the prime factorization of 300
300 = 2 x 2 x 3 x 5 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 14700 = 2 x 2 x 3 x 5 x 5 x 7 x 7
Step 4: Therefore, the least common multiple of 294 and 300 is 14700.
