Let's start with an example:
1/2 + 1/3
To add these two fractions, you first need to find the LCM which here is 6
Then you change both denominators to 6 and the problem becomes 3/6 + 2/6 = 5/6
Now if the LCM were 0, then you would get a denominator, 0. But you can not divide by 0. It becomes meaningless.
So the LCM always excludes 0
Shell program to find LCM and hcf of two no.s tput clear echo "Enter first no" read a echo "Enter 2nd no" read b p= 'expr $a \* $b' while [$b -ne 0] do r= 'expr $a % $b' a=$b b=$r done LCM = 'expr $p / $a' echo "LCM = $LCM" echo "Hcf = $a"
The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the numbers in the set. For sets of multiples, the LCM is the smallest number that is a multiple of all the numbers in the sets. The LCM can be calculated by finding the prime factorization of each number and then taking the highest power of each prime factor that appears in any of the numbers.
The LCM is a concept that makes sense for a set of non-zero integers. Otherwise, 0 is always the LCM of any set of numbers - even if none of them is 0.
Yes. If a x b = 0 then either a = 0, b = 0, or a = b = 0.
No.-------------------------------------------------------------To find the HCF and LCM of two (or more) numbers list the numbers in their prime factorisations in power format; then:HCF = product of the primes to the LOWEST power across all the numbers;LCM = product of the primes to the HIGHEST power across all the numbers.Note: for p being any prime, p⁰ = 1; so if a prime does not appear as a factor of a number, it can be said to have a power of 0. This means that the LOWEST power is 0 and the prime does not appear in the HCF of the numbers. The HIGHEST power of a prime must be at least the LOWEST power of a prime.Thus if a prime appears in the HCF of the numbers (with a power greater than or equal to 1) it MUST also appear in the LCM of the numbers.If the HCF of some numbers is 15, then: 15 = 3 × 5 which means that the primes 3 and 5 MUST both apear in the LCM.But 175 = 5² × 7, which does NOT include 3, so 175 CANNOT be the LCM of some numbers which have a HCF of 15.
#include<stdio.h> main() { int a,b,i,lcm,gcf; printf("\n Enter two numbers"); scanf("%d%d",&a,&b); for(i=0;i<=a;i++) { if((b%i==0)&&(a%i==0)) { gcf=i; } } lcm=a*b/gcf; printf("\n GCF is %d and LCM is %d",gcf,lcm); }
As a general principle, you can find the LCM of two numbers by dividing their product by their GCF. This one won't work. The product of any two numbers with 5 as a common factor would have to end in 5 or 0.
The LCM is not defined for any set of numbers that contains a zero.
Shell program to find LCM and hcf of two no.s tput clear echo "Enter first no" read a echo "Enter 2nd no" read b p= 'expr $a \* $b' while [$b -ne 0] do r= 'expr $a % $b' a=$b b=$r done LCM = 'expr $p / $a' echo "LCM = $LCM" echo "Hcf = $a"
#include<stdio.h> #include<conio.h> void lcm(int m,int n) { for(i=1;i++) { if(i%m==0&&i%n==0) return i; } } void main() { clrscr(); int a,b; a=19;b=20; printf("lcm is %d",lcm(a,b)); getch(); }
You can compare them by looking at them (they are the same)subtracting one from the other (answer = 0)dividing one by the other (the quotient is 1).
Because the LCM has to be a multiple of both numbers. A number can't have a multiple smaller than itself.
Least common multiples do not use zero as a multiple, as the LCM for any number and zero is zero.
The LCM is a concept that makes sense for a set of non-zero integers. Otherwise, 0 is always the LCM of any set of numbers - even if none of them is 0.
#include<stdio.h> #include<conio.h> void main() { int x,y,z,i; clrscr(); printf("Enter Two Numbers = "); scanf("d%d",&x,&y); for(i=1;i<=x*y*z;i++) { if(i%x==0&&i%y==0) { printf("LCM is %d\n",i); break; } } getch(); }
Yes. If a x b = 0 then either a = 0, b = 0, or a = b = 0.
LCM of 0 & 50 doesn't exist.