Least Common Multiple (LCM) of 68 and 112
The least common multiple (LCM) of 68 and 112 is 1904.
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 68 and 112?
First, calculate the GCD of 68 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 112 = 0 remainder 68 |
| 2 | 112 ÷ 68 = 1 remainder 44 |
| 3 | 68 ÷ 44 = 1 remainder 24 |
| 4 | 44 ÷ 24 = 1 remainder 20 |
| 5 | 24 ÷ 20 = 1 remainder 4 |
| 6 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 145 | 9715 |
| 115 and 174 | 20010 |
| 187 and 120 | 22440 |
| 178 and 33 | 5874 |
| 152 and 108 | 4104 |