Least Common Multiple (LCM) of 72 and 169
The least common multiple (LCM) of 72 and 169 is 12168.
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 72 and 169?
First, calculate the GCD of 72 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 169 = 0 remainder 72 |
| 2 | 169 ÷ 72 = 2 remainder 25 |
| 3 | 72 ÷ 25 = 2 remainder 22 |
| 4 | 25 ÷ 22 = 1 remainder 3 |
| 5 | 22 ÷ 3 = 7 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 32 | 1248 |
| 111 and 125 | 13875 |
| 102 and 11 | 1122 |
| 67 and 70 | 4690 |
| 14 and 144 | 1008 |