Least Common Multiple (LCM) of 78 and 169
The least common multiple (LCM) of 78 and 169 is 1014.
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 78 and 169?
First, calculate the GCD of 78 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 169 = 0 remainder 78 |
| 2 | 169 ÷ 78 = 2 remainder 13 |
| 3 | 78 ÷ 13 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 40 | 4360 |
| 111 and 192 | 7104 |
| 22 and 118 | 1298 |
| 20 and 119 | 2380 |
| 132 and 180 | 1980 |