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the LCM of 400 and 600​

Sagot :

Multiples of 400: 400, 800, 1200, 1600
Multiples of 600: 600, 1200, 1800

So the LCM is 1200
reinhard10158

Step-by-step explanation:

the LCM (least common multiple) is the product (multiplication) of the longest product strings of the prime factors.

prime factors of a number start with 2 (the smallest prime number). we keep dividing the number (and then the results) by 2 until the division is not delivering a whole number anymore. then we switch to the next higher prime number. and so on, until the result is 1.

prime factors of 400

400 : 2 = 200

200 : 2 = 100

100 : 2 = 50

50 : 2 = 25

25 : 2 no

25 : 3 no

25 : 5 = 5

5 : 5 = 1

the prime factorization of 400 is therefore

2×2×2×2×5×5

prime factors of 600

600 : 2 = 300

300 : 2 = 150

150 : 2 = 75

75 : 2 no

75 : 3 = 25

25 : 3 no

25 : 5 = 5

5 : 5 = 1

the prime factorization of 600 is therefore

2×2×2×3×5×5

the LCM is now the product of the longest multiplication chains for the prime factors :

the longest chain for 2 is

2×2×2×2 in 400

for 3 is

3 in 600

for 5 is

5×5 in 400 and 600

the LCM = 2×2×2×2 × 3 × 5×5 = 1,200.

which is much smaller than the "instinctive" product of 400 and 600 :

400×600 = 240,000

which is of course also a multiple of 400 and 600, but not the smallest one (LCM).

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