Least Common Multiple (LCM) of 68 and 73
The least common multiple (LCM) of 68 and 73 is 4964.
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 73?
First, calculate the GCD of 68 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 73 = 0 remainder 68 |
| 2 | 73 ÷ 68 = 1 remainder 5 |
| 3 | 68 ÷ 5 = 13 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 52 | 9100 |
| 145 and 152 | 22040 |
| 160 and 28 | 1120 |
| 10 and 42 | 210 |
| 53 and 176 | 9328 |