Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6 and 19 the smallest integer that is 114 that is divisible by both numbers.
Least Common Multiple (LCM) of 6 and 19 is 114.
LCM(6,19) = 114
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 6 and 19. First we will calculate the prime factors of 6 and 19.
Prime Factorization of 6
2 | 6 |
3 | 3 |
1 |
Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:
6 = 21×31
Prime Factorization of 19
19 | 19 |
1 |
Prime factors of 19 are 19. Prime factorization of 19 in exponential form is:
19 = 191
Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 19.
LCM(6,19) = 21×31×191
LCM(6,19) = 114
Factors of 6
List of positive integer factors of 6 that divides 6 without a remainder.
1, 2, 3, 6
Factors of 19
List of positive integer factors of 19 that divides 19 without a remainder.
1, 19
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 19, than apply into the LCM equation.
GCF(6,19) = 1
LCM(6,19) = ( 6 × 19) / 1
LCM(6,19) = 114 / 1
LCM(6,19) = 114
(i) The LCM of 19 and 6 is associative
LCM of 6 and 19 = LCM of 19 and 6
1. What is the LCM of 6 and 19?
Answer: LCM of 6 and 19 is 114.
2. What are the Factors of 6?
Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.
3. What are the Factors of 19?
Answer: Factors of 19 are 1, 19. There are 2 integers that are factors of 19. The greatest factor of 19 is 19.
4. How to Find the LCM of 6 and 19?
Answer:
Least Common Multiple of 6 and 19 = 114
Step 1: Find the prime factorization of 6
6 = 2 x 3
Step 2: Find the prime factorization of 19
19 = 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 114 = 2 x 3 x 19
Step 4: Therefore, the least common multiple of 6 and 19 is 114.