Question

If a,b and c are three natural numbers such that abc= 3600 , HCF(a,b,c)= 2, HCF(a,b) =10, HCF(b,c)=2 and HCF(a,c)=6 then what is LCM(a,b,c) equal to??

Answer 1

abc=3600
hcf(a,b,c)=2
hcf(a,b)=10
hcf(b,c)=6
lcm(a,b,c)=3600

Answer 2

Answer:

The LCM is 60.

Step-by-step explanation:

Given : If a,b and c are three natural numbers such that

abc= 3600 ,

HCF(a,b,c)= 2,

HCF(a,b) =10,

HCF(b,c)=2 and

HCF(a,c)=6

To find : LCM(a,b,c)

Solution :

For 3 numbers the relation between LCM and HCF and product  is

$a\times b\times c=\frac{(LCM(a,b,c)\times HCF(a,b)\times HCF(b,c)\times HCF(c,a)}{HCF (a,b,c)}$

To find LCM(abc),

$LCM(a,b,c)=\frac{(abc)\times HCF (a,b,c)}{HCF(a,b)\times HCF(b,c)\times HCF(c,a)}$

Substitute the value given,

$LCM(a,b,c)=\frac{3600\times 2}{10\times 2\times 6}$

$LCM(a,b,c)=\frac{7200}{120}$

$LCM(a,b,c)=60$

Therefore, The LCM is 60.