Question
Determine the lowest common multiple (LCM) of 12 and 18
Ask by Lyons Hodgson. in South Africa
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The lowest common multiple (LCM) of 12 and 18 is 36.
Solution
PROGRAM CalculateLCM
VAR
a : INT := 12;
b : INT := 18;
gcd : INT;
lcm : INT;
tempA : INT;
tempB : INT;
r : INT;
END_VAR
(* Compute the Greatest Common Divisor (GCD) using Euclid's algorithm *)
tempA := a;
tempB := b;
WHILE tempB <> 0 DO
r := tempA MOD tempB;
tempA := tempB;
tempB := r;
END_WHILE;
gcd := tempA;
(* Calculate the Lowest Common Multiple (LCM) *)
lcm := (a * b) / gcd;
(* After execution, lcm will hold the value 36, which is the LCM of 12 and 18 *)
END_PROGRAM
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Explain 
Simplify this solution Bonus Knowledge
To find the lowest common multiple (LCM) of 12 and 18, first identify their prime factors. For 12, the factors are 2² × 3, and for 18, they are 2 × 3². Now, the LCM takes the highest power of each prime factor: 2² (from 12) and 3² (from 18). So, LCM = 2² × 3² = 4 × 9 = 36. The lowest common multiple of 12 and 18 is 36. To visualize this concept, you can think of it as finding a common playground where both sets of children (12 and 18) can play together at intervals. The LCM represents the earliest time when both groups reunite to swing on the swings or slide down the slides together! It’s all about striking the right balance so everyone can play.
