Question

find the LCM of84,112,196​

Answer 1

The procedure to find the LCM of 84, 112, and 196 is as follows:

1. Decompose the numbers into their prime factors

84 |2

42|2

21|3

7 |7

1|

112 |2

56| 2

28 |2

14 |2

7 |7

1|

196 |2

98 |2

49| 7

7 |7

1|

2. Express the numbers as the product of their prime factors

• Prime factors of 84 = 2². 3. 7
• Prime factors of 112 = 2⁴. 7
• Prime factors of 196 = 2². 7²

3. Select the common and uncommon prime factors with the greatest exponent

Select the common and uncommon prime factors with the greatest exponentCommon prime factors: 2, 7

• Common prime factors with the greatest exponent: 2⁴, 7²
• Uncommon prime factors: 3
• Uncommon prime factors with the greatest exponent: 3¹

4. Calculate the Least Common Multiple or LCM

. Calculate the Least Common Multiple or LCMRemember that to find the LCM of several numbers, the common and uncommon prime factors must be multiplied with the greatest exponent.

$\boxed{ \bold{LCM = 2⁴, 7², 3¹ = 2352}}$