/* BC program john is a coded version of a recent algorithm of
   John Campbell. It is meant to be run with the BC program gcd
   which contains the functions gcd(a,b) and lcma(a[],n).
   johna(a[],n) takes an array of positive integers aa[0],...,aa[n-1]
   and replaces them by an array of positive integers a[0],...,a[n-1], 
   where
    (i) a[i] divides aa[i] for 0<=i<n;
   (ii) gcd(a[i],a[j])=1 for 0<=i<j<n;
   (iii) lcm(aa[0],...,aa[n-1])=lcm(a[0],...,a[n-1]).
   19th February 2003
 */

/* john(a,b) solves the problem for n=2 and is used in johna(a[],n). */

define john(a,b){
auto d,h,lcm

d=gcd(a,b)
if(d==1){
	john1=a
	john2=b
	lcm=a*b
}else{
	john1 = a/d
	h = gcd(john1,b)
	lcm = john1*b
	john2 = b
	while(h>1){
	   john1 = john1*h 
	    john2 = john2/h 
	    h = gcd(john1,john2)
	}
}
return(lcm)
}
 
define johna(aa[],n){
auto i,j,a[],t,temp

for(i=0;i<n;i++){
a[i]=aa[i]
}
for(j=1;j<n;j++){
	for(i=0;i<j;i++){
		temp=john(a[i],a[j])
		a[i]=john1
		a[j]=john2
	}
}
print "lcm("
for(i=0;i<n-1;i++){
	print aa[i],","
}
print aa[n-1],")="
print "lcm("
for(i=0;i<n-1;i++){
	print a[i],","
}
print a[n-1],")="
t=lcma(a[],n)
return(t)
}