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 301 the smallest integer that is 12642 that is divisible by both numbers.
Least Common Multiple (LCM) of 294 and 301 is 12642.
LCM(294,301) = 12642
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 294 and 301. First we will calculate the prime factors of 294 and 301.
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 301
7 | 301 |
43 | 43 |
1 |
Prime factors of 301 are 7,43. Prime factorization of 301 in exponential form is:
301 = 71×431
Now multiplying the highest exponent prime factors to calculate the LCM of 294 and 301.
LCM(294,301) = 21×31×72×431
LCM(294,301) = 12642
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 301
List of positive integer factors of 301 that divides 301 without a remainder.
1, 7, 43, 301
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 294 and 301, than apply into the LCM equation.
GCF(294,301) = 7
LCM(294,301) = ( 294 × 301) / 7
LCM(294,301) = 88494 / 7
LCM(294,301) = 12642
(i) The LCM of 301 and 294 is associative
LCM of 294 and 301 = LCM of 301 and 294
1. What is the LCM of 294 and 301?
Answer: LCM of 294 and 301 is 12642.
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 301?
Answer: Factors of 301 are 1, 7, 43, 301. There are 4 integers that are factors of 301. The greatest factor of 301 is 301.
4. How to Find the LCM of 294 and 301?
Answer:
Least Common Multiple of 294 and 301 = 12642
Step 1: Find the prime factorization of 294
294 = 2 x 3 x 7 x 7
Step 2: Find the prime factorization of 301
301 = 7 x 43
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12642 = 2 x 3 x 7 x 7 x 43
Step 4: Therefore, the least common multiple of 294 and 301 is 12642.