Question

learning goal 2.2: students will find the least common multiple (lcm) in mathematical and real world contexts. find the least common multiple (lcm) of each pair of numbers 1. 12 and 15 2. 7 and 11 3. 35 and 5 4. 24 and 16

Explanation:

Step1: Find LCM of 12 and 15

Prime factorize 12: $12 = 2^2 \times 3$
Prime factorize 15: $15 = 3 \times 5$
LCM is product of highest powers: $2^2 \times 3 \times 5 = 60$

Step2: Find LCM of 7 and 11

7 and 11 are primes. LCM of primes is their product: $7 \times 11 = 77$

Step3: Find LCM of 35 and 5

Prime factorize 35: $35 = 5 \times 7$
Prime factorize 5: $5 = 5$
LCM is the larger number (since 35 is a multiple of 5): $35$

Step4: Find LCM of 24 and 16

Prime factorize 24: $24 = 2^3 \times 3$
Prime factorize 16: $16 = 2^4$
LCM is highest power of 2 and 3: $2^4 \times 3 = 48$

Answer:

1. 60
2. 77
3. 35
4. 48