Least Common Multiple (LCM) of 156 and 177
The least common multiple (LCM) of 156 and 177 is 9204.
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 156 and 177?
First, calculate the GCD of 156 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 177 = 0 remainder 156 |
| 2 | 177 ÷ 156 = 1 remainder 21 |
| 3 | 156 ÷ 21 = 7 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 89 | 10680 |
| 69 and 27 | 621 |
| 109 and 144 | 15696 |
| 111 and 167 | 18537 |
| 169 and 98 | 16562 |