Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 30 and 49 the smallest integer that is 1470 that is divisible by both numbers.
Least Common Multiple (LCM) of 30 and 49 is 1470.
LCM(30,49) = 1470
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 30 and 49. First we will calculate the prime factors of 30 and 49.
Prime Factorization of 30
2 | 30 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:
30 = 21×31×51
Prime Factorization of 49
7 | 49 |
7 | 7 |
1 |
Prime factors of 49 are 7. Prime factorization of 49 in exponential form is:
49 = 72
Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 49.
LCM(30,49) = 21×31×51×72
LCM(30,49) = 1470
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1, 2, 3, 5, 6, 10, 15, 30
Factors of 49
List of positive integer factors of 49 that divides 49 without a remainder.
1, 7, 49
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30 and 49, than apply into the LCM equation.
GCF(30,49) = 1
LCM(30,49) = ( 30 × 49) / 1
LCM(30,49) = 1470 / 1
LCM(30,49) = 1470
(i) The LCM of 49 and 30 is associative
LCM of 30 and 49 = LCM of 49 and 30
1. What is the LCM of 30 and 49?
Answer: LCM of 30 and 49 is 1470.
2. What are the Factors of 30?
Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.
3. What are the Factors of 49?
Answer: Factors of 49 are 1, 7, 49. There are 3 integers that are factors of 49. The greatest factor of 49 is 49.
4. How to Find the LCM of 30 and 49?
Answer:
Least Common Multiple of 30 and 49 = 1470
Step 1: Find the prime factorization of 30
30 = 2 x 3 x 5
Step 2: Find the prime factorization of 49
49 = 7 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1470 = 2 x 3 x 5 x 7 x 7
Step 4: Therefore, the least common multiple of 30 and 49 is 1470.