Question

Find the least no that is divisible by all natural number from 1 to 10

Answer 1

Answer: 2520

Step-by-step explanation:

Find the L.C.M of nos from 1 to 10. The answer you will get is 2520. It is easier if you can memorise these simple nos, it will be easier for you will help in saving your time.

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Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★Here we have to find LCM :-

1 = 1

2 = 2

3 = 3

4 = 2²

5 = 5

$\begin{array}{r | 1} 2 & 6 \\ \cline{2-2} & 3 \end{array}$

7 = 7

$\begin{array}{r | 1} 2 & 8 \\ \cline{2-2} 2 & 4 \\ \cline{2-2} & 2 \end{array}$

9 = 3²

10 = 2 × 5

LCM = 2³ × 3² × 5 × 7 = 2520

${\boxed{\sf\:{Additional\; Information}}}$

In case :-

★Three positive integers a,b,c

★HCF(a,b,c) × LCM(a,b,c) ≠ a × b × c

$\tt{\rightarrow LCM(a,b,c)=\dfrac{a\times b\times c\times HCF (a,b,c)}{HCF(a,b)\times HCF(b,c)\times HCF(a,c)}}$

$\tt{\rightarrow HCF(a,b,c) =\dfrac{a\times b\times c\times LCM (a,b,c)}{LCM(a,b)\times LCM(b,c)\times LCM(a,c)}}$