The Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both. For 1200 and 800, the LCM is 4,800.
How to Find the LCM
There are different methods to find the LCM of two numbers. Let’s explore the two most common ones:
1. Prime Factorization Method
In this method, we find the prime factors of each number, then take the highest power of each prime that appears in either factorization.
- Prime factors of 1200:
1200=24×3×521200 = 2^4 \times 3 \times 5^21200=24×3×52 - Prime factors of 800:
800=25×52800 = 2^5 \times 5^2800=25×52
Now, take the highest powers of each prime:
- For 222, the highest power is 252^525
- For 333, we take 313^131 (appears only in 1200)
- For 555, the highest power is 525^252
Multiply them together:
LCM=25×31×52=4800LCM = 2^5 \times 3^1 \times 5^2 = 4800LCM=25×31×52=4800
2. Division Method
In the division method, we divide the numbers by their common prime factors until we reach 1.
- Step 1: Divide both numbers by 2.
1200÷2=6001200 \div 2 = 6001200÷2=600, 800÷2=400800 \div 2 = 400800÷2=400 - Step 2: Divide again by 2.
600÷2=300600 \div 2 = 300600÷2=300, 400÷2=200400 \div 2 = 200400÷2=200 - Step 3: Divide again by 2.
300÷2=150300 \div 2 = 150300÷2=150, 200÷2=100200 \div 2 = 100200÷2=100 - Step 4: Divide again by 2.
150÷2=75150 \div 2 = 75150÷2=75, 100÷2=50100 \div 2 = 50100÷2=50 - Step 5: Divide both numbers by 3 (since 75 is divisible by 3).
75÷3=2575 \div 3 = 2575÷3=25, 505050 remains the same. - Step 6: Divide both numbers by 5.
25÷5=525 \div 5 = 525÷5=5, 50÷5=1050 \div 5 = 1050÷5=10 - Step 7: Divide again by 5.
5÷5=15 \div 5 = 15÷5=1, 10÷5=210 \div 5 = 210÷5=2 - Step 8: Divide by 2.
2÷2=12 \div 2 = 12÷2=1
Now, multiply all divisors:
LCM=25×3×52=4800LCM = 2^5 \times 3 \times 5^2 = 4800LCM=25×3×52=4800
Conclusion
The LCM of 1200 and 800 is 4,800, and you can find it using either the prime factorization method or the division method. Both give the same result