Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7 and 16 the smallest integer that is 112 that is divisible by both numbers.
Least Common Multiple (LCM) of 7 and 16 is 112.
LCM(7,16) = 112
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 7 and 16. First we will calculate the prime factors of 7 and 16.
Prime Factorization of 7
7 | 7 |
1 |
Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:
7 = 71
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 7 and 16.
LCM(7,16) = 24×71
LCM(7,16) = 112
Factors of 7
List of positive integer factors of 7 that divides 7 without a remainder.
1, 7
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 7 and 16, than apply into the LCM equation.
GCF(7,16) = 1
LCM(7,16) = ( 7 × 16) / 1
LCM(7,16) = 112 / 1
LCM(7,16) = 112
(i) The LCM of 16 and 7 is associative
LCM of 7 and 16 = LCM of 16 and 7
1. What is the LCM of 7 and 16?
Answer: LCM of 7 and 16 is 112.
2. What are the Factors of 7?
Answer: Factors of 7 are 1, 7. There are 2 integers that are factors of 7. The greatest factor of 7 is 7.
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 7 and 16?
Answer:
Least Common Multiple of 7 and 16 = 112
Step 1: Find the prime factorization of 7
7 = 7
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 = 112 = 2 x 2 x 2 x 2 x 7
Step 4: Therefore, the least common multiple of 7 and 16 is 112.