The number of ordered pairs of positive integers having 30 as their LCM is?
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I started by taking two numbers such as 2257111322571113and 2357111323571113. The LCM of those two numbers is 2357111323571113. Similarly, If I take two numbers like 23−x57−y1113−z23−x57−y1113−z and 2357111323571113, the LCM is 2357111323571113. Here 0≤x≤30≤x≤3, 0≤y≤70≤y≤7, 0≤z≤130≤z≤13
The number of ways of choosing 3 numbers x,y,zx,y,zis 4C1⋅8C1⋅14C14C1⋅8C1⋅14C1
The above value is only for b=23571113b=23571113.But now I have to consider another value of bb and the the solution becomes lengthy. Is this the correct approach?
The number of ways of choosing 3 numbers x,y,zx,y,zis 4C1⋅8C1⋅14C14C1⋅8C1⋅14C1
The above value is only for b=23571113b=23571113.But now I have to consider another value of bb and the the solution becomes lengthy. Is this the correct approach?
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