HCF /LCM For more than two numbers

MBA CAT 2023
1

When we have more than two numbers, the formula- product of two numbers=HCF* LCM doesn’t work. How can we find the third number when we know HCF, LCM of three numbers and Two numbers, Following the above approach? Or could you suggest a better o…

2

When we have more than two numbers, the formula- product of two numbers=HCF* LCM doesn't work.
How can we find the third number when we know HCF, LCM of three numbers and Two numbers, Following the above approach? Or could you suggest a better one.?

3

while solving one problem i faced issue with this LCM formula

LCM of fractions = LCM of numerators / HCF of denominators

Method1 :

I was to find LCM of 1.2 and 2.

1.2 = (12/10)

2=(2/1)

LCM of [(12/10),(2/1)]=[LCM of (12,2)]/[HCF of(10,1)]

LCM of (12,2) = LCM of [{(2^2)*3},2]/[HCF of(2*5,1)]

But

LCM of [{(2^2)*3},2]=(2^2)*3 =12

[HCF of(2*5,1)]=1

therefore,

LCM of (1.2,2)=12/1 = 12 (which is wrong)

Method2 :

1.2 = (12/10)

2=(12/6)

LCM of [(12/10),(12/6)]=[LCM of (12,12)]/[HCF of(10,6)]

But

LCM of [12,12]=12

[HCF of(10,6)]=HCF of(2*5,2*3)=2

LCM of (1.2,2)=12/2 = 6 (which is correct)

But I did not get what wrong am I doing in Method 1 ?