gr 6 maths - lcm
2. Find the LCM of the following numbers by prime factor method.
168, 180 and 330
3. Find the LCM of 72, 90, 108 using prime factor method.
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Answers
2.The instructions to find the LCM of 168, 180 and 330 are the next:
1. Decompose all numbers into prime factors
168 -2 84 -2 42- 2 21 3 7 7 1 180 2 90 2 45 3 15 3 5 5 1 330 2 165 3 55 5 11 11 1
2. Write all numbers as the product of its prime factors
Prime factors of 168 = 23 . 3 . 7
Prime factors of 180 = 22 . 32 . 5
Prime factors of 330 = 2 . 3 . 5 . 11
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 2 , 3
Common prime factors with the greatest exponent: 23, 32
Uncommon prime factors: 7 , 5 , 11
Uncommon prime factors with the greatest exponent: 71, 51, 111
4. Calculate the Least Common Multiple or LCM
Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.
LCM = 23. 32. 71. 51. 111 = 27720
3.
Decompose all numbers into prime factors
72 2 36 2 18 2 9 3 3 3 1 90 2 45 3 15 3 5 5 1 108 2 54 2 27 3 9 3 3 3 1
2. Write all numbers as the product of its prime factors
Prime factors of 72 = 23 . 32
Prime factors of 90 = 2 . 32 . 5
Prime factors of 108 = 22 . 33
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 2 , 3
Common prime factors with the greatest exponent: 23, 33
Uncommon prime factors: 5
Uncommon prime factors with the greatest exponent: 51
4. Calculate the Least Common Multiple or LCM
Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.
LCM = 23. 33. 51 = 1080
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