Question

Find the LCF.
(i) 12, 15
(ii) 6, 8, 10
(iii) 18, 32
(iv) 10, 15, 20
(v) 45, 86
(vi) 15, 30, 90
(vii) 105, 195
(viii) 12, 15, 45
(ix) 63, 81
(x) 18, 36, 27

Answer 1

Answer:

1)60

2)480

3)576

4)60

5)3872

6)90

7)20475

8)1080

9)5103

10)216

Answer 2

$\large{\bigstar \; \rm{\pink{Solutions:}}}$

Find the LCF:

• 12, 15

                      $\Large{ \begin{array}{c|c|c} \tt 3 & \sf \orange{12 } & \sf\orange{ 15 }\\ \tt 5 & \sf \orange{4 }& \sf \orange{5} \\ \tt 4 & \sf \orange{4 }& \sf \orange{1 }  \\ & \sf \orange{1 } & \sf \orange{1 }\end{array}}$

LCM = 3 × 5 × 4 = 60

• 6, 8, 10  

                        

LCM = 2 × 3 × 4 × 5​ = 120

• 18, 32

                      $\Large{ \begin{array}{c|c|c} \tt 2 & \sf \orange{18 } & \sf\orange{ 32 }\\ \tt 9 & \sf \orange{9 }& \sf \orange{16} \\ \tt 16 & \sf \orange{1 }& \sf \orange{16} \\ & \sf \orange{1 }& \sf \orange{1 }\end{array}}$  

LCM = 2 × 9 × 16 ​= 288

• 10, 15, 20

                      [tex]\Large{ \begin{array}{c|c|c|c} \tt 2 & \sf \orange{10 } & \sf\orange{ 15 } & \orange{ 20} \\ \tt 5 & \sf \orange{5 }& \sf \orange{15}& \orange{ \sf 10} \\ \tt 2 & \sf \orange{1 }& \sf \orange{3} &\orange{ \sf 2} \\\tt 3 & \sf \orange{1 }& \sf \orange{3 } & \orange{ \sf 1} \\& \orange{ \sf 1} & \orange{ \sf 1} & \orange{ \sf 1}\end{array}}[/tex]

LCM = 2 × 2 × 3 × 5 =  60

• 45, 86

                      $\Large{ \begin{array}{c|c|c} \tt 45 & \sf \orange{45 } & \sf\orange{ 86 }\\ \tt 86 & \sf \orange{1 }& \sf \orange{86} \\ & \sf \orange{1 }& \sf \orange{1 }\end{array}}$

LCM = 45 × 86 = 3870

• 15, 30, 90

                      $\Large{ \begin{array}{c|c|c|c} \tt 2 & \sf \orange{15 } & \sf\orange{ 30} & \orange{ \sf 90} \\ \tt 3 & \sf \orange{15 }& \sf \orange{15} & \orange{ \sf 45} \\ \tt 5 & \sf \orange{5}& \sf \orange{5} &\orange{ \sf 15} \\ \tt 3 & \sf \orange{1 }& \sf \orange{1 } & \orange{ \sf 3} \\ & \orange{ \sf 1} & \orange{ \sf 1} & \orange{ \sf 1}\end{array}}$

LCM = 2 × 3 × 3 × 5 = 90

• 105, 195

                      [tex] \Large{ \begin{array}{c|c|c} \tt 3 & \sf \orange{105 } & \sf\orange{ 195 }\\ \tt 5 & \sf \orange{35 }& \sf \orange{65} \\ \tt 7 & \sf \orange{7 }& \sf \orange{13}\\ \tt 13 & \orange{\sf 1} & \orange{\sf 13} \\ & \sf \orange{1 }& \sf \orange{1 }\end{array}}[/tex]  

LCM = 3 × 5 × 7 × 13 = 1365

• 12, 15, 45

                      [tex]\Large{ \begin{array}{c|c|c|c} \tt 3 & \sf \orange{12 } & \sf\orange{ 15} & \orange{ \sf 45} \\ \tt 2 & \sf \orange{4 }& \sf \orange{5}& \orange{ \sf 15} \\ \tt 2 & \sf \orange{2}& \sf \orange{5} &\orange{ \sf 15} \\ \tt 3 & \sf \orange{1 }& \sf \orange{5 }  & \orange{ \sf 15} \\ \tt 5 & \orange{\sf 1 } & \orange{\sf 1} & \orange{\sf 5}\\& \orange{ \sf 1} & \orange{ \sf 1} & \orange{ \sf 1}\end{array}}[/tex]

LCM = 2 × 2 × 3 × 3 × 5 = 180

• 63, 81

                      $\Large{ \begin{array}{c|c|c} \tt 3 & \sf \orange{63 } & \sf\orange{ 81} \\ \tt 3 & \sf \orange{21 }& \sf \orange{27}  \\ \tt 3 & \sf \orange{7}& \sf \orange{5} \\ \tt 3 & \sf \orange{7 }& \sf \orange{3 } \\ \tt 7 & \orange{\sf 7 } & \orange{\sf 1} \\ & \orange{ \sf 1} & \orange{ \sf 1}\end{array}}$

LCM = 3 × 3 × 3 × 3 × 5 = 567

• 18, 36, 27

                       $\Large{ \begin{array}{c|c|c|c} \tt 2 & \sf {\orange{18 }} & \sf{\orange{ 36}} & \orange{\sf 27} \\ \tt 2 & \sf {\orange{9 }}& \sf {\orange{18}} & \orange{\sf 27} \\ \tt 3 & \sf{ \orange{9}}& \sf {\orange{9}} & \orange{\sf 27} \\ \tt 3 & \sf{ \orange{3 }}& \sf {\orange{3 }} & \orange{\sf 9} \\ \tt 3 & \orange{\sf 1 } & \orange{\sf 1} & \orange{\sf 3} \\ & \orange{ \sf 1} & \orange{ \sf 1} & \orange{ \sf 1}\end{array}}$

​LCM = 2 × 2 × 3 × 3 × 3 = 108