Least Common Multiple (LCM) of 16 and 137
The least common multiple (LCM) of 16 and 137 is 2192.
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 16 and 137?
First, calculate the GCD of 16 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 137 = 0 remainder 16 |
| 2 | 137 ÷ 16 = 8 remainder 9 |
| 3 | 16 ÷ 9 = 1 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 47 | 4371 |
| 179 and 128 | 22912 |
| 136 and 88 | 1496 |
| 115 and 40 | 920 |
| 179 and 18 | 3222 |