What is the LCM of 109 and 60?

What is the LCM of 109 and 60? The answer is 6540. LCM using prime factorisation, common factor, video tutorial & instructions for each step.

How do I solve what is the lcm of 109 and 60??

Follow our step-by-step animated guide that breaks down the problem into simple, easy-to-understand steps.

What is LCM of 109, 60 | Prime factorisation, common factor

Prime Factorization Method

There are multiple ways to find the least common multiple of given integers. In this method, we find the prime factors of each number, and then take the highest power of each prime that appears in the factorization of either number for find LCM.

Find the prime factorization of each number:

109 = 109

60 = 2, 2, 3, 5

Identify the highest powers of all prime numbers that appear in the factorization: $2^2 × 3^1 × 5^1 × 109^1$
To find LCM multiply these highest powers: LCM(109, 60) = $2^2 × 3^1 × 5^1 × 109^1$ = 6540

🎬Watch the Step-by-Step Animated Solution

Watch the process of finding the least common multiple of 109 and 60. Our animation shows multiple approaches, including listing multiples and using prime factorization, making it easy to understand this fundamental concept through visual demonstration.

What You'll Learn:

Calculate the least common multiple of 109 and 60
Learn different strategies: listing multiples and using prime factorization
Understand the relationship between LCM and GCF

Visual learners (65% of students) can watch the lcm process unfold rather than trying to imagine it from static text.

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📖 Why This Specific Problem Matters

This animated solution addresses a critical gap in mathematics education: while teachers can demonstrate a few examples in class, students often struggle when practicing problems with different numbers at home. Our step-by-step animation for 109 lcm 60 provides instant, visual support for this EXACT problem - not just similar ones. This specificity is crucial for building confidence and understanding, especially for visual learners who need to see the process, not just read about it.

Step-by-step breakdown: Our animation breaks down 109 lcm 60 into clear, sequential steps that build understanding from foundation to solution.

Listing All Common Factors Method

To find the Least Common Multiple (LCM) of 109 and 60 using the method of listing common multiples, follow these steps:

List some multiples of each number.
Identify the smallest multiple that is common to both lists.

Multiples of 109

109, 218, 327, 436, 545, 654, 763, 872, 981, 1090,…

Multiples of 60

60, 120, 180, 240, 300, 360, 420, 480, 540, 600,…

Common multiples

Identify the common multiples from the lists above: 6540, 13080,…

The smallest common multiple is 6540.

The LCM of 109 and 60 using the common multiples method is 6540.

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🌍 Real-World Example

Real-world example for 109 lcm 60

Teaching Tip

💡 Teaching tip: Practice this lcm problem with objects around you to understand it better!

🔗 Related Concept

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📚 Difficulty Level: Grade 6-8: Middle School

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What is the LCM of 109 and 60?

Answer: The LCM of 109 and 60 is 6540