Question

what is the lcm of 14 ,26 and 91​

Answer 1

Answer:

182

Step-by-step explanation:

Given numbers : 14, 26 and 91

Prime Factorisation of 14 :

→ 2 × 7 × 1

→ 2¹ × 7¹ × 1¹

Prime Factorisation of 26 :

→ 2 × 13 × 1

→ 2¹ × 13¹ × 1¹

Prime Factorisation of 91 :

→ 7 × 13 × 1

→ 7¹ × 13¹ × 1¹

____________________________

• LCM : Least Common Factor

It can be calculated as : Multiplication of highest power of any number in the prime factorisation.

____________________________

LCM(14, 26, 91) = 2¹ × 7¹ × 13¹ × 1¹

→ 2 × 7 × 13 × 1

→ 182

Answer 2

AnswEr :

$\underline{\bigstar\:\textsf{Solving \: with \: Method \: 1 :}}$

$\bullet$ Find, the L.C.M (least common factor) of all number together.

$\begin{array}{r | l} 2 & 14, 26, 91 \\ \cline{1-2}7 & 7, 13, 91 \\ \cline{1-2} 13 & 1, 13, 13 \\ \cline{1-2} & 1, 1, 1 \end{array}$

$\normalsize\ : \implies\sf\ L.C.M = 2 \times\ 7 \times\ 13 \\ \\ \normalsize\ : \implies\sf\ L.C.M = 182$

$\normalsize\ : \implies{\boxed{\sf \green{L.C.M(14,26,91) = 182}}}$

$\underline{\bigstar\:\textsf{Solution \: with \: method \: 2: }}$

$\bullet$ In this one, first we find the prime factorization of triad numbers as given (i.e. 14,26,91) and then collect common multiples from them.

1)Prime factorization of 14 :-

$\begin{array}{r | l} 2 & 14 \\ \cline{1-2} 7 & 7 \\ \cline{1-2} & 1 \end{array}$

$\normalsize\ : \implies\sf\ 14 = 2 \times\ 7 \times\ 1$

2)Prime factorization of 26 :-

$\begin{array}{r | l} 2 & 26 \\ \cline{1-2} 13 & 13 \\ \cline{1-2} & 1 \end{array}$

$\normalsize\ : \implies\sf\ 26 = 2 \times\ 13 \times\ 1$

3)Prime factorization of 91 :-

$\begin{array}{r | l} 7 & 91 \\ \cline{1-2} 13 & 13\\ \cline{1-2} & 1 \end{array}$

$\normalsize\ : \implies\sf\ 91 = 7 \times\ 13 \times\ 1$

$\rule{100}{1}$

$\bullet$ Common multiples = 2,7,13.So,

$\normalsize\ : \implies\sf\ L.C.M = 2 \times\ 7 \times\ 13 \times\ 1 \\ \\ \normalsize\ : \implies\sf\ L.C.M = 182$

$\normalsize\ : \implies{\boxed{\sf \blue{L.C.M(14,26,91) = 182}}}$