Question

Solve the following question using Matlab language only.

Least common multiple (LCM) of two numbers is the smallest number that they both divide. For example, the LCM of 2 and 3 is 6, as both numbers can evenly divide the number 6. Find the LCM of two numbers using recursion Hint: You may assume that the first number is always smaller than the second number. Examplel First number for LCM:3 Second number for LCM 19 The LCM of 3 and 19: 57 Example2 First number for LCM:6 Second number for LCM 12 The LCM of 6 and 12: 12 The greatest common divisor (GCD) of two or more integers is the largest positive integer that divides each of the integers. For example, the GCD of 8 and 12 is 4. Find the GCD of two numbers using recursion Hint: You may assume that the first number is always smaller than the second number. Examplel First number for GCD: 2 Second number for GCD: 10 The GCD of 2 and 10 is 2 Example2 First number for GCD: 10 Second number for GCD: 50 The GCD of 10 and 50 is 10

Answer 1

$\color{blue}\underline{gcd.m:}$

A = input("First number for GCD: ");
B = input("Second number for GCD: ");
result = 1;
i = 1;
while(i <= A && i <= B)
if(mod(A,i) == 0 && mod(B,i)==0)
result = i;
end
i = i + 1;
end
  
fprintf("The GCD of %d and %d is %d\n",A,B,result)

$\color{red}\underline{Output:}$

octave:1> soucc("gcd.m") First number for GCD: 2 Second number for GCD: >10 The GCD of 2 and 10 is 2 octave:2> source("gcd.m") First number for GCD: 10 Second number for GCD: 50 The GCD of 10 and 50 is 10

$\color{blue}\underline{lcm.m:}$

A = input("First number for LCM: ");
B = input("Second number for LCM: ");
result = 1;
i = 1;
while(i <= A && i <= B)
if(mod(A,i) == 0 && mod(B,i)==0)
result = i;
end
i = i + 1;
end
  
fprintf("The LCM of %d and %d is %d\n",A,B,(A*B)/result);

$\color{red}\underline{Output:}$

octave :1> source("їст.m") First number for LCM: >3 Second number for LCM: 19 The LCM of 3 and 19 is 57 octave :2> source("їст.m") First number for LCM: > 6 Second number for LCM: 12 The LCM of 6 and 12 is 12

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