Least Common Multiple (LCM) of 157 and 69
The least common multiple (LCM) of 157 and 69 is 10833.
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 157 and 69?
First, calculate the GCD of 157 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 69 = 2 remainder 19 |
| 2 | 69 ÷ 19 = 3 remainder 12 |
| 3 | 19 ÷ 12 = 1 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 23 | 759 |
| 188 and 86 | 8084 |
| 164 and 140 | 5740 |
| 15 and 112 | 1680 |
| 154 and 152 | 11704 |