If a=pl.qm.rn and b=px.qy.rz where p,q,r are primes and p<q<r and l,m,n,x,y,z are all natural numbers. Given HCF = p2.q3.r and LCM = p3.q4.r3, which one of the following is NOT true?
If a=pl.qm.rn and b=px.qy.rz where p,q,r are primes and p<q<r and l,m,n,x,y,z are all natural numbers. Given HCF = p2.q3.r and LCM = p3.q4.r3, which one of the following is NOT true?
The correct option is D l + m + n = x + y + z
HCF = Product of the smallest powers of each common prime factor in the numbers.
= pmin(l,x).qmin(m,y).rmin(n,z)
Where min(l,x) is the value which is minimum between l and x.
LCM = Product of the largest powers of each common prime factor in the numbers.
= pmax(l,x).qmax(m,y).rmax(n,z)
Where max(l,x) is the value which is maximum between l and x.
We can not say which among l and x is maximum, but we can be sure that between l and x, one of them is minimum and the other is maximum, so l + x = 2 + 3 = 5
m + y = 7
n + z = 4
and l + m + n ≠ x + y + z
l + m + n = x + y + z
HCF = Product of the smallest powers of each common prime factor in the numbers.
= pmin(l,x).qmin(m,y).rmin(n,z)
Where min(l,x) is the value which is minimum between l and x.
LCM = Product of the largest powers of each common prime factor in the numbers.
= pmax(l,x).qmax(m,y).rmax(n,z)
Where max(l,x) is the value which is maximum between l and x.
We can not say which among l and x is maximum, but we can be sure that between l and x, one of them is minimum and the other is maximum, so l + x = 2 + 3 = 5
m + y = 7
n + z = 4
and l + m + n ≠ x + y + z
