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 16 the smallest integer that is 48 that is divisible by both numbers.
Least Common Multiple (LCM) of 6 and 16 is 48.
LCM(6,16) = 48
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 16. First we will calculate the prime factors of 6 and 16.
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 16
2 | 16 |
2 | 8 |
2 | 4 |
2 | 2 |
1 |
Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:
16 = 24
Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 16.
LCM(6,16) = 24×31
LCM(6,16) = 48
Factors of 6
List of positive integer factors of 6 that divides 6 without a remainder.
1, 2, 3, 6
Factors of 16
List of positive integer factors of 16 that divides 16 without a remainder.
1, 2, 4, 8, 16
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 16, than apply into the LCM equation.
GCF(6,16) = 2
LCM(6,16) = ( 6 × 16) / 2
LCM(6,16) = 96 / 2
LCM(6,16) = 48
(i) The LCM of 16 and 6 is associative
LCM of 6 and 16 = LCM of 16 and 6
1. What is the LCM of 6 and 16?
Answer: LCM of 6 and 16 is 48.
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 16?
Answer: Factors of 16 are 1, 2, 4, 8, 16. There are 5 integers that are factors of 16. The greatest factor of 16 is 16.
4. How to Find the LCM of 6 and 16?
Answer:
Least Common Multiple of 6 and 16 = 48
Step 1: Find the prime factorization of 6
6 = 2 x 3
Step 2: Find the prime factorization of 16
16 = 2 x 2 x 2 x 2
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 48 = 2 x 2 x 2 x 2 x 3
Step 4: Therefore, the least common multiple of 6 and 16 is 48.