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 302 the smallest integer that is 44394 that is divisible by both numbers.
Least Common Multiple (LCM) of 294 and 302 is 44394.
LCM(294,302) = 44394
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 302. First we will calculate the prime factors of 294 and 302.
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 302
2 | 302 |
151 | 151 |
1 |
Prime factors of 302 are 2,151. Prime factorization of 302 in exponential form is:
302 = 21×1511
Now multiplying the highest exponent prime factors to calculate the LCM of 294 and 302.
LCM(294,302) = 21×31×72×1511
LCM(294,302) = 44394
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 302
List of positive integer factors of 302 that divides 302 without a remainder.
1, 2, 151, 302
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 294 and 302, than apply into the LCM equation.
GCF(294,302) = 2
LCM(294,302) = ( 294 × 302) / 2
LCM(294,302) = 88788 / 2
LCM(294,302) = 44394
(i) The LCM of 302 and 294 is associative
LCM of 294 and 302 = LCM of 302 and 294
1. What is the LCM of 294 and 302?
Answer: LCM of 294 and 302 is 44394.
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 302?
Answer: Factors of 302 are 1, 2, 151, 302. There are 4 integers that are factors of 302. The greatest factor of 302 is 302.
4. How to Find the LCM of 294 and 302?
Answer:
Least Common Multiple of 294 and 302 = 44394
Step 1: Find the prime factorization of 294
294 = 2 x 3 x 7 x 7
Step 2: Find the prime factorization of 302
302 = 2 x 151
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 44394 = 2 x 3 x 7 x 7 x 151
Step 4: Therefore, the least common multiple of 294 and 302 is 44394.