Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 16 and 31 the smallest integer that is 496 that is divisible by both numbers.
Least Common Multiple (LCM) of 16 and 31 is 496.
LCM(16,31) = 496
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 16 and 31. First we will calculate the prime factors of 16 and 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
Prime Factorization of 31
31 | 31 |
1 |
Prime factors of 31 are 31. Prime factorization of 31 in exponential form is:
31 = 311
Now multiplying the highest exponent prime factors to calculate the LCM of 16 and 31.
LCM(16,31) = 24×311
LCM(16,31) = 496
Factors of 16
List of positive integer factors of 16 that divides 16 without a remainder.
1, 2, 4, 8, 16
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1, 31
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16 and 31, than apply into the LCM equation.
GCF(16,31) = 1
LCM(16,31) = ( 16 × 31) / 1
LCM(16,31) = 496 / 1
LCM(16,31) = 496
(i) The LCM of 31 and 16 is associative
LCM of 16 and 31 = LCM of 31 and 16
1. What is the LCM of 16 and 31?
Answer: LCM of 16 and 31 is 496.
2. 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.
3. What are the Factors of 31?
Answer: Factors of 31 are 1, 31. There are 2 integers that are factors of 31. The greatest factor of 31 is 31.
4. How to Find the LCM of 16 and 31?
Answer:
Least Common Multiple of 16 and 31 = 496
Step 1: Find the prime factorization of 16
16 = 2 x 2 x 2 x 2
Step 2: Find the prime factorization of 31
31 = 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 496 = 2 x 2 x 2 x 2 x 31
Step 4: Therefore, the least common multiple of 16 and 31 is 496.