Question

If HCF(a,b) = 12 and a*b = 1800 then LCM(a,b) is
a.3600
b.900
c.150
d.90

Answer 1

Hint: We are given the HCF of two numbers and the product of two numbers . By using the property HCF * LCM = Product of the two numbers ( a * b ) we can find the LCM of the two numbers

Complete step-by-step answer:
We are given that the Highest Common Factor of two numbers a and b is 12
And the product of the two numbers is 1800
Let the Least Common Multiple of the numbers a and b be x
We know that for any two numbers a and b
HCF * LCM = Product of the two numbers ( a * b )
From this we get,
$
   \Rightarrow 12*x = 1800 \\
   \Rightarrow 12x = 1800 \\
   \Rightarrow x = \dfrac{{1800}}{{12}} = 150 \\
$
Therefore the lcm of a and b is 150
The correct option is c.

Note: 1.H.C.F of given numbers always divides their L.C.M
2. H.C.F of given fractions = H.C.F of numerator / L.C.M of denominator
3. L.C.M of given fractions = L.C.M of numerator / H.C.F of denominator
4. If d is the H.C.F of two positive integer a and b, then there exist unique integer m and n, such that d = am + bn
5. If p is prime and a,b are any integer then P/ ab ,This implies P/a or P/b
6. H.C.F of a given number always divides its L.C.M