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Question Number 188970 by BaliramKumar last updated on 09/Mar/23

$$\mathrm{LCM}(x,144,150)=10800howmanyvalueofx.$$$$$$

Answered by mr W last updated on 10/Mar/23

$$10800=2^4\times 3^3\times 5^2$$$$144=2^4\times 3^2$$$$150=2\times 3\times 5^2$$$$x=2^{0-4}\times 3^3\times 5^{0-2}$$$$\Rightarrow thereare5\times 3=15possiblevalues$$$$forx.$$

Commented by BaliramKumar last updated on 10/Mar/23

$$Thanks$$

Commented by BaliramKumar last updated on 10/Mar/23

$$pleaseexplainlaststep$$

Commented by mr W last updated on 10/Mar/23

$$x=a\times 3^3\times b$$$$a=(2^0,2^1,2^2,2^3,2^4)$$$$b=(5^0,5^1,5^2)$$$$ahas5possibilities$$$$bhas3possibilities$$$$sox=a\times 3^3\times bhas5\times 3=15possibilities.$$

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