Least Common Multiple (LCM) of 112 and 64
The least common multiple (LCM) of 112 and 64 is 448.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 112 and 64?
First, calculate the GCD of 112 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 64 = 1 remainder 48 |
| 2 | 64 ÷ 48 = 1 remainder 16 |
| 3 | 48 ÷ 16 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 176 | 23408 |
| 156 and 111 | 5772 |
| 183 and 80 | 14640 |
| 108 and 119 | 12852 |
| 97 and 98 | 9506 |