Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2974 and 2980 the smallest integer that is 4431260 that is divisible by both numbers.
Least Common Multiple (LCM) of 2974 and 2980 is 4431260.
LCM(2974,2980) = 4431260
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 2974 and 2980. First we will calculate the prime factors of 2974 and 2980.
Prime Factorization of 2974
2 | 2974 |
1487 | 1487 |
1 |
Prime factors of 2974 are 2,1487. Prime factorization of 2974 in exponential form is:
2974 = 21×14871
Prime Factorization of 2980
2 | 2980 |
2 | 1490 |
5 | 745 |
149 | 149 |
1 |
Prime factors of 2980 are 2, 5,149. Prime factorization of 2980 in exponential form is:
2980 = 22×51×1491
Now multiplying the highest exponent prime factors to calculate the LCM of 2974 and 2980.
LCM(2974,2980) = 22×51×1491×14871
LCM(2974,2980) = 4431260
Factors of 2974
List of positive integer factors of 2974 that divides 2974 without a remainder.
1, 2, 1487, 2974
Factors of 2980
List of positive integer factors of 2980 that divides 2980 without a remainder.
1, 2, 4, 5, 10, 20, 149, 298, 596, 745, 1490, 2980
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2974 and 2980, than apply into the LCM equation.
GCF(2974,2980) = 2
LCM(2974,2980) = ( 2974 × 2980) / 2
LCM(2974,2980) = 8862520 / 2
LCM(2974,2980) = 4431260
(i) The LCM of 2980 and 2974 is associative
LCM of 2974 and 2980 = LCM of 2980 and 2974
1. What is the LCM of 2974 and 2980?
Answer: LCM of 2974 and 2980 is 4431260.
2. What are the Factors of 2974?
Answer: Factors of 2974 are 1, 2, 1487, 2974. There are 4 integers that are factors of 2974. The greatest factor of 2974 is 2974.
3. What are the Factors of 2980?
Answer: Factors of 2980 are 1, 2, 4, 5, 10, 20, 149, 298, 596, 745, 1490, 2980. There are 12 integers that are factors of 2980. The greatest factor of 2980 is 2980.
4. How to Find the LCM of 2974 and 2980?
Answer:
Least Common Multiple of 2974 and 2980 = 4431260
Step 1: Find the prime factorization of 2974
2974 = 2 x 1487
Step 2: Find the prime factorization of 2980
2980 = 2 x 2 x 5 x 149
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4431260 = 2 x 2 x 5 x 149 x 1487
Step 4: Therefore, the least common multiple of 2974 and 2980 is 4431260.