Best Answer

If you have the gcd or the LCM of two numbers, call them a and b, you can use the relationship that gcd(a,b) = (a multiplied by b) divided by LCM (a,b) where LCM or gcd (a,b) means the LCM or a and b. This means the gcd multiplied by the LCM is the same as the product of two numbers.

Let's assume you have neither.

There are several ways to do this. One way to approach both problems at once is to factor each number into primes. You can use these prime factorizations to find both the LCM and gcd

To compute the Greatest common divisor, list the common prime factors and raise each to the least multiplicities that occurs among the several whole numbers.

To compute the least common multiple, list all prime factors and raise each to the greatest multiplicities that occurs among the several whole numbers.

Study guides

☆☆

Q: Compute the gcd and LCM of two numbers?

Write your answer...

Submit

Still have questions?

Related questions

First, calculate the greatest common divisor (gcd) of both numbers. The following recursive function achieves that: int gcd (int a, int b) { if (!a || !b) return 0; if (a==b) return a; // base case if (a>b) return gcd(a-b, b); return gcd(a, b-a); } Now we can compute the lcm from the gcd: int lcm (int a, int b) { return (a / gcd(a, b)) * b; }

no

If you have two numbers m and n and their gcd (or gcf), g then their LCM = m*n/g so LCM = 72*252/36 = 2*252 = 504.

You need at least two numbers to find either of those.

The following function will return the GCD or LCM of two arguments (x and y) depending on the value of the fct argument (GCD or LCM). enum FUNC {GCD, LCM}; int gcd_or_lcm(FUNC fct, int x, int y) { int result = 0; switch (fct) { case (GCD): result = gcd (x, y); break; case (LCM): result = lcm (x, y); break; } return result; }

Only if they're the same number. The LCM and GCF of 10 and 10 is 10.

(start) [calculate gcd] [calculate product] [divide] (stop)

For this you will need a couple of helper algorithms. The first is the GCD (greatest common divisor) which is expressed as follows:procedure GCD (a, b) isinput: natural numbers a and bwhile ab doif a>blet a be a-belselet b be b-aend ifend whilereturn aThe second algorithm is the LCM (least common multiple) of two numbers:procedure LCM (a, b) isinput: natural numbers a and b return (a*b) / GCD (a, b)Now that you can calculate the GCD and LCM of any two natural numbers, you can calculate the LCM of any three natural numbers as follows:procedure LCM3 (a, b, c) isinput: natural numbers a, b and c return LCM (LCM (a, b), c)Note that the LCM of three numbers first calculates the LCM of two of those numbers (a and b) and then calculates the LCM of that result along with the third number (c). That is, if the three numbers were 8, 9 and 21, the LCM of 8 and 9 is 72 and the LCM of 72 and 21 is 504. Thus the LCM of 8, 9 and 21 is 504.

You can just use the GCD of any two of your numbers and find the GCD of it with your third number. Same for LCM. public class Lcmgcd { private static int gcd(int a, int b) { return (b == 0) ? a: gcd(b, a%b); } private static int lcm(int a, int b) { return a * b / gcd(a, b); } public static void main(String[] args) { int[] n = {12, 16, 28}; System.out.println("GCD: " + gcd(n[2], gcd(n[0], n[1])) + "\tLCM: " + lcm(n[1],lcm(n[2],n[0]))); } }

The LCM of any two numbers can be found with the following formula:LCM(a,b) = (ab) / GCD (a,b).The GCD of two numbers is best found with the Euclidean algorithm which is as follows:GCD(a,b) =a --if b = 0or GCD(b, a mod b) otherwiseIn the example given we have GCD(42,7) = GCD(7, 0) = 7Then LCM(42,7) = (7*42)/7 = 42Note: mod is the operation of dividing one number by another and taking the remainder. e.g. 7 mod 4 = 3, 12 mod 6 = 0.

If we multiply the gcd and the LCM, we get the numbers.Call the numbers a and b. So 16(LCM)=ab3584=ab let's all the LCM, x 16x=a(3584/a)using the information above.x= 1/16(3584)or x=224 So the LCM is 224 we can just say the (gcd)LCM=ab=3584, so just divide 3584 by 16.

Hey Friends here is the program of HCF and LCM with output:Statement of C Program: Find The LCM and HCF of Two Numbers :#include #includevoid main(){int num1 , num2 , lcm , gcd , remainder , numerator , denominator ;clrscr();printf( "Enter two numbers\n");scanf(" %d%d " , &num1 , &num2 );if (num1 > num2){numerator=num1;denominator=num2;}else{numerator = num2 ;denominator = num1 ;}remainder = num1 % num2;while ( remainder != 0){numerator = denominator;denominator = remainder;remainder = numerator % denominator;}gcd = denominator;lcm = (num1 * num2 ) / gcd;printf("GCD of %d and %d =%d\n" , num1, num2, gcd);printf(" LCM of %d and %d= %d\n" , num1, num2, lcm);getch();}Output:Enter two numbers515GCD of 5 and 15 = 5LCM of 5 and 15 = 15

People also asked